Research Interests

Differential and integral geometry and its applications to other fields such as mathematical relativity, convexity, and, most recently, number theory.

Education

• Ph.D.  California Institute of Technology  (1982)
• M.S.  California State University, Northridge (1974)
• B.A.  California State University, Northridge (1973)

Experience

• Professor, University of South Carolina (1999 – present)
• Associate Professor, University of South Carolina (1988 – 1999)
• Assistant Professor, University of South Carolina (1984–1988)
• Research Associate, Michigan State University (1982–1984)
• Visiting Assistant Professor, Duke University (Fall 1987)
• Visiting Associate Professor, Royal Institute of Technology, Stockholm (Fall 1993 & Spring 1994)

Courses Taught

• MATH 122: Calculus for Business Administration and Social Sciences
• MATH 172: Mathematical Modeling for the Life Sciences
• MATH 174: Discrete Mathematics for Computer Science
• MATH 141: Calculus I
• MATH 142: Calculus II
• MATH 241: Vector Calculus
• MATH 242: Elementary Differential Equations
• MATH 250: Honors Vector Calculus
• MATH 300: Transition to Advanced Mathematics
• MATH 520: Ordinary Differential Equations
• MATH 521: Boundary Value Problems and Partial Differential Equations
• MATH 511: Probability
• MATH 523: Mathematical Modeling of Population Biology
• MATH 524: Nonlinear Optimization
• MATH 527: Numerical Analysis
• MATH 531: Foundations of Geometry
• MATH 546: Algebraic Structures I
• MATH 532: Modern Geometry
• MATH 550: Vector Analysis
• MATH 551: Introduction to Differential Geometry
• MATH 552: Applied Complex Variables
• MATH 554: Analysis I
• MATH 555: Analysis II
• MATH 574: Discrete Mathematics I
• MATH 580: Elementary Number Theory
• MATH 700: Graduate Linear Algebra
• MATH 701: Algebra I
• MATH 705: Analysis III
• MATH 723: Advanced Differential Equations
• MATH 726: Numerical Analysis I
• MATH 727: Numerical Analysis II
• MATH 732: Algebraic Topology I
• MATH 733: Algebraic Topology II
• MATH 734: Differential Geometry
• MATH 738: Differential Topology
• MATH 739: Complex Geometry II
• MATH 748: The Symmetric Group and its Representations
• MATH 748: Groups and Graph

Selected Publications

• Mohammad Ghomi and Ralph Howard
  Total diameter and area of closed submanifolds. Mathematische Annalen
  363 (2015), no. 3-4, 985–999.
• Mohammad Ghomi and Ralph Howard
  Tangent cones and regularity of real hypersurfaces. Journal für die Reine und
  Angewandte Mathematik. [Crelle's Journal] Math. 697 (2014), 221–247.
• Ralph Howard
  Convex bodies of constant width and constant brightness. Advances in Mathematics
  204 (2006), no. 1, 241–261.
• Aaron Abrams, Jason Cantarellai Joseph H. G, Fu, Mohammad Ghomi, and Ralph Howard
  Circles minimize most knot energies. Topology 42 (2003), no. 2, 381–394
• P. T. Chruściel, E. Delay, G. J. Galloway, and R. Howard
  Regularity of horizons and the area theorem. Annales Henri Poincaré. A Journal of
  Theoretical and Mathematical Physics 2 (2001), no. 1, 109–178.
• Lars Andersson and Ralph Howard
  Comparison and rigidity theorems in semi-Riemannian geometry. Communications in
  Analysis and Geometry 6 (1998), no. 4, 819–877.
• Ralph Howard
  The kinematic formula in Riemannian homogeneous spaces. Memoirs of the American
  Mathematical Society 106 (1993), no. 509, vi+69 pp.
• Ralph Howard and Anton Schep
  Norms of positive operators on \(L^p\)-spaces. Proceedings of the American Mathematical
  Society 109 (1990), no. 1, 135–146.