Curriculum Vitae
Oscar Mario Perdomo
Department of Mathematics, Central Connecticut State University
Home Address: 139 Saint James St.
West Hartford, CT 06119
Office phone number: (860) 832 2848
e-mail: [email protected]
Field of Specialization:
Differential Geometry and Differential Equations
Professional preparation:
Universidad del Valle at Cali-Colombia
Universidad del Valle at Cali-Colombia
Indiana University at Bloomington
University of California at Irvine
B.A. , Math. 03/1994
M.A. , Math. 07/1995
Ph. D. Math. 07/2000
Postdoctoral Institution 09/00-07/01
Appointments:
09/2016
09/2011
01/2008
06/2007
09/2006
08/2003
08/2001
09/2000
09/1995
09/1995
-
Present
08/2016
08/2011
12/2007
05/2007
08/2006
07/2003
07/2001
07/2000
07/2000
Central Connecticut State University, Full Professor
Central Connecticut State University, Associate Professor
Central Connecticut State University, Assistant Professor
Universidad del Valle, Professor
Lehigh University, Visiting Assistant Professor
Universidad del Valle, Associate Professor
Universidad del Valle, Assistant Professor
University of California at Irvine, Visiting Assistant Professor
Indiana University, Teaching Assistant
Universidad del Valle, Teaching Assistant
Awards:
3. System-wide Board of Regents Research Award 2014. Award given to recognize faculty from the
state universities who are doing exceptional research and creative work.
2. Best Young Mathematician of Colombia. July 2004. Award given by the TWAS foundation
(Third World Academic Science) and the Academia Colombiana de Ciencias Exactas Físicas y
Naturales. Award given every 4 years to Mathematicians under 40 in Colombia.
1. Award by Mazda Company. Junio 1993- Junio 1995: Grant to pursue graduate studies given to
the best 10 top Colombian undergraduate students of Music and Science.
Published Papers:
[41] Perdomo, O., Wei, G n-dimensional area of minimal rotational hypersurfaces in spheres. Nonlinear Anal. 125 (2015), p. 241-251.
[40] Perdomo, O., Wei, G A characterization of quadric constant Gauss-Kronecker curvature hypersurfaces of spheres. Asian J. Math. 19 (2015), no. 2, p. 251-264.
[39] Perdomo, O. Constant speed ramps Pacific J. Math. 275 (2015), no 1, p. 1-18.
[38] Palmer, B., Perdomo, O. Rotating drops with helicoidal symmetry Pacific J. Math. 273 (2015),
no 2, p. 413-441.
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[37] Perdomo, O., Wei, G A characterization of quadric constant scalar curvature hypersurfaces of
spheres. J. Geom. Anal. 24 (2014), no 4, p. 1882-1890.
[36] Perdomo, O. Helicoidal minimal surfaces in R3 , Illinois J. Math. Vol 57 (2013) no. 1, 87-104.
[35] Perdomo, O. Algebraic constant mean curvature surfaces in Euclidean space, Houston J. Math.
Vol 39 (2013) no. 1, 127-136.
[34] Perdomo, O., Brasil, A Stability index jump for CMC hypersurfaces of spheres, Arch. Math.
(Basel) Vol 99 (2012), no. 5, 493-500.
[33] Perdomo A dynamical interpretation of the profile curve of cmc Twizzlers surfaces, Pacific
Journal of Mathematics, Vol 258, No. 2, (2012), p. 459-485.
[32] Perdomo, O. CMC hypersurfaces on riemannian and semi-riemannian manifolds, Math. Phys.
Anal. Geom. 15 (2012), no. 1 p. 17-37.
[31] Perdomo, O. Algebraic zero mean curvature varieties in semi-riemannian manifolds, Geom.
Dedicata 152 (2011), 183-196.
[30] Johnson, Perdomo Minimal tori with low nullity J. Math. Anal. Appl. 380 (2011) no. 1,
163-176.
[29] Perdomo, O. Embedded cmc hypersurfaces on hyperbolic spaces, Rev. Colombiana Mat. 45
(2011) no. 1, 81-96.
[28] Perdomo, O. Superficies con curvatura media constante, Bol Mat. Vol 18, No 2, pp 157-182,
2011.
[27] Perdomo, O. Embedded constant mean curvature hypersurfaces on spheres, Asian J. Math.
Vol 14, No 1, pp 73-108, March 2010.
[26] Perdomo, O. New examples of maximal space like surfaces in the anti-de Sitter space. J. Math.
Anal. Appl. 353 (2009), no. 1, 403–409.
[25] Alias, Brasil, Perdomo, O. A characterization of quadratic constant mean curvature hypersurfaces of spheres. Journal of Geometric Analysis 18 no 3, (2008) 687–703.
[24] Perdomo, O. Characterization of order 3 algebraic immersed minimal surfaces of S 3 . Geom.
Dedicata 129 (2007), 23–34.
[23] Perdomo, O. Metrics on products of surfaces with non positive sectional curvature. Israel
Journal of Mathematics 156 (2006) 65–71.
[22] Alias, Brasil, Perdomo Stable constant mean curvature hypersurfaces in the real projective
space. Manuscripta Math 121 (2006), no. 3, 329–338.
[21] Alias, Brasil, Perdomo On the stability index of hypersurfaces with constant mean curvature
in spheres. Proc. Amer. Math. Soc. 135. (2007), no. 11 3685–3693.
[20] Mesa, Perdomo Hipervariedades mínimas algebraicas en S n . Rev. Un. Mat. Argentina 47
(2006), no. 2, 67–75.
[19] Perdomo, O. Non-existence of regular algebraic surfaces of spheres of degree 3. J. Geom. 84
(2005), no. 1-2, 100–105.
[18] Arango, J. & Perdomo, O Morse Theory for semianalytic functions. J. Geom. 84 (2005), no.
1-2, 13–22.
[17] Perdomo, O. Distribution of minimal varieties in spheres in terms of the coordinate functions.
Rocky Mountain J.Math. Vol 35, No 1 (2005), pp 227-233.
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[16] Perdomo, O. On the average of the scalar curvature for minimal hypersurfaces of spheres with
low index. Illinois Journal of Mathematics. Vol 48, No 2, Summer 2004. pp. 559-565.
[15] Perdomo, O. Rigidity of minimal hypersurfaces with two principal curvartures. Archiv Mathematik. 82 (2004) 180-184.
[14] Perdomo, O. First eigenvalue characterization of Clifford hypersurfaces. Proc. Amer. Math.
Soc. Vol 130, No 11 (2002): pages. 3379-3384.
[13] Perdomo, O. Low index minimal hypersurfaces of spheres Asian Journal of Mathematics, Vol
5, No 4 : 715-724. 2001.
[12] Perdomo, O. sobre el nacimiento de la geometría riemanniana. Revista Tumbaga 3. (2008),
157–173.
[11] Montaño, Perdomo, Salas Métricas planas y el teorema de uniformización en toros mínimos de
la esfera unidad 3 dimensional. Rev. Acad. Colombiana Cienc. Exact. Fis Natur. 32. (2008) no.
123, 235–243.
[10] Perdomo, O. Minimal Torus invariant under one reflection. Mat. Ensen. Univ Esp. Issue,
(2007) pp. 11–16.
[9] Perdomo, O. Minimal hypersurfaces in Rn as regular values of a function. Rev. Integr. Temas
mat. 22. (2004), no. 1-2, 1–6.
[8] Perdomo, O. Nonembeddability of the Klein Bottle in RP 3 and Lawson’s Conjecture. Rev.
Acad. Colombiana Cienc. Exact. Fís. Natur. 29 (2005), no. 110, 149–154.
[7] Perdomo, O. Another proof for the rigidity of Clifford minimal hypersurfaces of S n . Matemáticas:
Enseñanza Universitaria. Vol. XIII. No. 4. Junio de (2005), 91–97.
[6] Perdomo, O. Rigidity of minimal hypersurfaces of spheres with constant ricci curvarure. Rev.
Colombiana Mat. 38 (2004), no. 2, 73–85.
[5]. Perdomo O. Mathematical foundations of a surface made out of triangles. Revista Epiciclos
Vol 4 No 1 (2005), 77–87 .
[4] Perdomo, O. Gráficas de funciones sobre variedades. Matemáticas: Enseñanza Universitaria.
Vol. XII. No. 1. Junio de 2004, pp. 21-26.
[3] Perdomo, O. Stable minimal hypersurfaces in R8 and R9 with constant scalar curvature. Revista
Colombiana de Matemáticas. Vol 36, No 2, (2002) pp. 96-106.
[2] Perdomo, O. Totally geodesic surfaces and the Hopf’s conjecture. Matematicas: Ensenanza
Universitaria, Vol. X No 1,2 Dic. (2002), pp. 29-35.
[1] Perdomo, O. La aplicación de Gauss de una superficie mínima completa y lagrangiana no puede
omitir más de 4 puntos Memorias III Escuela de Verano, Universidad de los Andes, 20 al 30 de junio
de 1995. Pages 33-40.
Preprints:
[7] Perdomo, O. A family of periodic solutions of the three body problem. Light version (Posted
online at: http://arxiv.org/pdf/1509.04981.pdf)
[6] Perdomo, O. A small variation of the Taylor Method and periodic solutions of the 3-body problem
(Posted online at: http://arxiv.org/pdf/1507.01100.pdf )
[5] Perdomo, O. A family of Solutions of the N-Body Problem
(Posted online at: http://arxiv.org/pdf/1410.1757.pdf )
[4] Lopez, R., Perdomo, O. Minimal Translation surfaces in Euclidean space
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[3] Palmer, B., Perdomo, O. Equilibrium shapes of cylindrical rotating drops (To appear, Bulletin
of the Brazilian Mathematical Society)
[2] Perdomo, O. Rotational surfaces in S 3 with constant mean curvature. (To appear, Journal of
Geometric Analysis)
[1] Castaneda, Perdomo Order two algebraic minimal hypersurfaces in the hyperbolic space
Talks:
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Movimientos periódicos y la noción de número real: Buscando soluciones del problema de los tres cuerpos
Universidad Icesi, Cali, Colombia. Sep. 30, 2015.
A small variation of the Taylor Method and periodic solutions of the three body problem.
CCSU Department of Mathematics Colloquium. Feb. 20, 2015.
A characterization of non-planar solutions of the 3-Body problem with one body moving on a line.
BYU-Brigham Young University, Department de Mathematics. Dec. 2, 2014.
Salto del índice de estabilidad de hipersuperficies con curvatura media constante en esferas.
Universidad de Murcia, Departamento de Matemáticas. Dec. 11, 2014.
Minimal translation surfaces in the Euclidean space.
CCSU Department of Mathematics Colloquium. Sep. 19, 2014.
Rotating drops with helicoidal surface.
Spring Easter Sectional AMS Meeting, Baltimore, Maryland. March. 29, 2014.
CCSU Department of Mathematics Colloquium. Feb. 7, 2014.
Friction keeping constant speed on 3-D ramps.
CCSU Department of Mathematics Colloquium. Sept. 13, 2013.
Friction keeping constant speed.
CCSU Department of Mathematics Colloquium. March 15, 2013.
A characterization of quadric constant scalar curvature hypersurfaces of spheres.
CCSU Department of Mathematics Colloquium. March 1, 2013.
Surfaces in R3 with constant mean curvature.
PDE and Differential Geometry Seminar, UCONN, Stors, CT, October 1, 2012.
Embedded constant mean curvature hypersurfaces on spheres.
XVII Escola de Geometria Diferencial. Manaus, AM, Brazil. Julio 20, 2012.
South China Normal University, Guangzhou, P.R. China. May 22, 2013.
Idaho State University, Pocatello, ID, USA. April 5, 2013.
Rotationally symmetric embedded surfaces with constant mean curvature in the
three-dimensional unit sphere.
• CCSU Department of Mathematics Colloquium. Sept. 07, 2012.
24. Constant mean curvature course and Plenary.
• Workshop in Geometric Analysis, Universidade Federal Do Ceara, Fortaleza, Brazil,
January 30-February 3, 2012.
23. Two remarks on the two bodies problem
• CCSU Department of Mathematics Colloquium. December. 02, 2011.
22. 2. The φ-TreadmillSled of a curve.
• CCSU Colloquium of Mathematics, March 4, 2011
21. 3. A dynamical interpretation of the profile curve of cmc Twizzlers surfaces
• Universidad de Granada, at Granada Spain. Feb 17, 2011
• Clavius Differential Geometry seminar, Fairfield University. July 6, 2012
20. Hypersurfaces of space forms with constant mth curvature.
• University of Notre Dame, IN. November 6, 2010.
19. The Hopf conjecture.
• CCSU Department of Mathematics Colloquium. Sept. 03, 2010
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18. Constant mean curvature surfaces in the Euclidean space and their dynamical interpretation.
• CCSU Department of Mathematics Colloquium. Feb. 05, 2010
• St. Mary’s College of Maryland. March 24, 2010
• CCSU at the 13th Connecticut State University Faculty Research Conference. April. 17, 2010
17. Algebraic minimal hypersurfaces of order two in the hyperbolic space
• CCSU Department of Mathematics Colloquium. Sep. 11, 2009
16. Embedded CMC hypersurfaces on spheres and other spaces
• Lehigh University Geometry and Topology Conference. June 05, 2009
• XVII Colombian Congress of Mathematics CCM, Aug. 03, 2009
15. Embedded CMC hypersurfaces on spheres
• St. Mary’s College of Maryland. March 24, 2010
• Indiana University, Differential Geometry Seminar. April. 16, 2009
• CCSU Department of Mathematics Colloquium. March 20, 2009
14. Examples of zero mean curvature varieties in de Sitter and Anti de Sitter spaces.
• CCSU Physics Club, Robert F. Voytek Memorial Lecture Series, March 05, 2009
13. The birth of Riemannian geometry.
• CCSU Department of Mathematics Colloquium. Oct. 17, 2008
12. Minimal tori with low nullity
• American Mathematical Society Meeting held at Indiana University. April. 05, 2008
11. Maximal space-like surfaces in the Anti de Sitter 3-dimensional space.
• CCSU Department of Mathematics Colloquium. March. 28, 2008
10. Minimal algebraic surfaces of spheres
• CCSU Department of Mathematics Colloquium. Feb. 01, 2008
9. A family of solutions for the sihn-Gordon equation
• VII Americas School in Differential Equations and Nonlinear Analysis. July. 27, 2007
8. Minimal surfaces in S 3 with Natural nullity less than 8
• Lehigh Math Colloquium, Lehigh University, USA. Feb. 28, 2007
7. Stability index of CMC hypersurfaces of spheres
• XIV conferencia de geometria diferencial en Salvador Bahia, Brasil. Jun. 27, 2006
6. On the existence of minimal hypersurfaces of spheres
• II Encuentro de geometría Diferencial in La Falda, Argentina. Jun. 27, 2005
5. The average of the scalar curvature for minimal hypersurfaces of spheres with low index
• XIII conferencia de geometria diferencial en Sao Paulo, Brasil. Jun. 27, 2004
4. Low index minimal hypersurfaces of Spheres
• Stanford University, Geometry Analysis Seminar. Nov. 4, 1998
• Indiana University, Differential Geometry Seminar. Feb. 18, 1999
• University of Illinois at Urbana, Differential Geometry Seminar. March 28, 1999
• Universidad del Valle, Differental Geometry Seminar. June 28, 1999
3. A stability Characterization of Clifford hypersurfaces in S n
• Indiana University, Differential Geometry Seminar. Sep. 23, 1999
• UCIrvine, Differential Geometry Seminar. Oct 17, 2000
2. Conformal metric associated with a mechanical system
• Indiana University, Graduate Student Seminar. Feb. 1999
1. The Gauss map of a complete minimal lagrangian surface can not omit
more than four points
• Universidad de los Andes at Bogota-Col., Escuela de Verano, June 1995
Research projects:
6. Title: Periodic Solution of the Three Body Problem. Approved from June 2015 to June 2016.
This is a 2015 CSU Research Grant.
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6. Title: Trajectories of celestial bodies under special inertial frames. Approved from June 2014 to
June 2015. This is a 2014 CSU Research Grant.
5. Title: Shape of rotating drops. Approved from June 2013 to June 2014. This is 2013 a CSU
Research Grant.
4. Title: Maximal submanifold in Anti de Sitter Spaces. From January 2008 to May 2009. Project
Approved by CCSU.
3. Title: Algebraic minimal hypersurfaces of spheres. From February 2008 to May 2009. Project
financially supported by CCSU.
2. Title: Clasificación de hipervariedades mínimas en esferas. From March 2004 to March 2006.
Project financially supported by Colciencias (Colombian NSF) and Unversidad del Valle.
1. Title: Clasificación de Variedades área minimizadoras en R8 . From December 2001 to June
2003. Project financially supported by Colciencias (Colombian NSF) and Unversidad del Valle
Thesis Advisor and Postgraduate-Scholar Sponsor
Peter Li, University of California at Irvine, Postdoctoral sponsor
Bruce Solomon, Indiana University, PhD. thesis advisor
Carlos Rodriguez, Universidad del Valle, MA. thesis advisor
Students that have completed their degree under my supervision:
Graduate student: Steven Lemay. Name of thesis: New examples of zero mean curvature surfaces
in the three dimensional anti de-Sitter space. May 2012.
Graduate student: Edwin Barrios Rivera. Name of thesis: Variedades Isoparámetricas. August
2011.
Undergraduate student: Johann Suarez. Name of thesis: Análisis de superficies mínimas en S 3
cuando las divide un ecuador. August 2004.
Undergraduate student: Frank Suarez. Name of thesis: Toros mínimos en S 3 y la conjetura de Yau.
June 2004
Undergraduate student: Remigio Delgado. Name of thesis: esferas mínimas en S 3 . June 2005
Undergraduate student: Fabian Ramirez. Name of thesis: Hipersuperficies espaciales compactas
con curvatura media constante en los espacios de De Sitter. June 2006.
Undergraduate student: Ivan Gallardo. Name of thesis: Hipersuperficies mínimas en esferas con
dos curvaturas principales distintas. June 2006.
Graduate student: Lina Bonilla. Name of thesis: Superficies mínimas algebraicas de grado 4 en S 3 .
September 2007
Graduate student: Heber Mesa. Name of thesis: Superficies mínimas algebraicas de grado 4 en S 3 .
April 2006
Graduate student: Hector Guerrero. Name of thesis: Inmersiones mínimas de hipersurperfices en
esferas por primeras funciones propias. October 2006.