Ralph Elwood Howard

(This vita also available in DVI, and PDF formats.)
Department of Mathematics
University of South Carolina
Columbia, South Carolina 29208 USA
Office Phone: (803)-777-2913 Home Phone: (803)-799-8401
Citizenship: United States of America


Ph.D California Institute of Technology 1977-1982
M.S. California State University, Northridge 1973-1974
B.A. California State University, Northridge 1970-1973

Professional 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

Grant Support

1986 NSF Summer Support (though Department of Engineering) Michael A. Sutton, Principal Investor
1988-1990 NSF Summer Support, Co-Principal Investor with Marek Kossowski
1992 Summer Support on EPSCoR grant
1994-1999 Summer Support on DEPSCoR grants

Graduate Students

Master's Students:
1990 Somasundaram Velummylum, The Calculus of Variations and Zoll Surfaces.
1991 Louis Kenneth Reinitz, The Periodic Symmetry Groups of the Plane.
1991 Gary Allen Cohen, Intersection Theory.
1999 Aseem Raval, Mathematics Related to Spinning Tops.
2001 Michael S. Venn, Analysis on Finite Gel'fand Spaces.
2004 Anamaria Rusu, Reflection Groups.
Ph.D. Students:
1991 Shiying Zhao, On the Boundary Behavior of Subharmonic Functions in Nontangential Acessible Domains. (Supervised jointly with Manfred Stoll.)

Colloquium and Seminar Talks

1982 University of South Carolina
1984 Eastern Michigan State University
1984 Michigan State University
1985 University of Rochester (2 Talks)
1985 University of Oklahoma (2 Talks)
1986 University of Missouri
1988 University of North Carolina, Chapel Hill
1988 Emory University (2 Talks)
1988 Benedict College
1989 Saint Olaf College
1989 University of Minnesota
1990 University of Massachusetts, Amherst
1991 University of South Carolina, Aiken
1992 University of Utah
1992 Utah State University
1993 Dynamics Seminar Royal Institute of Technology, Stockholm
1993 Analysis Seminar Royal Institute of Technology, Stockholm
1994 Analysis Seminar University of Uppsala, Sweden
1994 Physics Seminar University of Stockholm
1994 University of Tennessee, Knoxville
1995 University of Miami
1996 Physics Department University of South Carolina
1997 University of Miami (2 Talks)
1999 University of Georgia
2001 University of Georgia
2001 Texas Tech (2 Talks)
2002 University of Georgia

Talks at Conferences

1984 Brunswick, Maine
1985 Los Angles, California
1987 San Antonio, Texas
1987 Salt Lake City, Utah
1987 Waterloo, Ontario, Canada
1989 Chapel Hill, North Carolina
1989 Corvallis, Oregon
1991 San Francisco, California
1992 Bethlehem, Pennsylvania
1992 Athens, Georgia
1992 Athens, Georgia
1994 Athens, Georgia
1996 Orlando, Florida
1996 Columbia, Missouri
1997 Memphis, Tennessee
1998 Athens, Georgia
1999 Birmingham, Alabama
1999 Athens, Georgia
2000 Lowell, Massachusetts
2001 Wichita, Kansas (Plenary Speaker)
2002 Pisa, Italy
2002 Boston, Massachusetts
2003 Baltimore, Maryland
2003 Charleston, South Carolina
2003 Lawrenceville, New Jersey
2004 Wuhan, China (Plenary Speaker)
2004 Snowbird, Utah
2006 San Antonio, Texas
2006 Norman, Oklahoma (Plenary Speaker)
2006 Oberwolfach, Geometry
2007 Baton Rouge, Louisiana
2007 New Orleans, Louisiana

Conferences Organized


  1. The kinematic formula in Riemannian homogeneous spaces Memoirs of the Amer. Math. Soc. Volume 109 Number 509 (1993)


  1. Dimension inequalities on the range of a multilinear function with vector space range Linear and Multilinear Algebra 8 (1978-1980) pp. 247-252
  2. Linear maps that preserve matrices annihilated by a polynomial Linear Algebra Appl. 30 (1980) pp. 167-176
  3. The nonexistence of stable submanifolds, verifolds, and harmonic maps in sufficiently pinched simply connected Riemannian manifolds Michigan Math. J. 32 (1985) pp. 321-334
  4. (with S. W. Wei) Inequalities relating sectional curvatures of a submanifold to the size of its second fundamental form and applications to pinching theorems for submanifolds Proc. Amer. Math. Soc. 94 (1985) pp. 699-702
  5. (with S. W. Wei) Nonexistence of stable harmonic maps to and from certain homogeneous spaces and submanifolds of Euclidean space Trans. Amer. Math. Soc. 294 (1986) pp. 319-331
  6. On the Gehrig link problem and the isoperimetric inequality of Bombieri and Simon J. Analyse Math. 47 (1986) pp. 243-253
  7. (with J. C. Bezdek, R.J. Hathaway, C. A. Wilson) Coordinate descent and clustering Control and Cybernet 15 (1986) pp. 195-204
  8. Classical integral geometry in Riemannian homogeneous spaces Contemporary Mathematics 63 (1987) pp. 179-203
  9. (with J. C. Bezdek, R.J. Hathaway, C. A. Wilson, M. P. Windham) Local convergence analysis of a grouped variable version of coordinate decent J. Optim. Theory Appl. 54 (1987) pp. 471-477
  10. A note on Roe's characterization of the sine function Proc. Amer. Math. Soc. 105 (1989) pp. 658-663
  11. (with R. A. DeVore, C. Micchelli) Optimal nonlinear approximation Manuscripta Math. 63 (1989) pp. 469-478
  12. (with P. R. Goodey) Processes of flats induced by higher dimensional processes Advances in Math. 80 (1990) pp. 92-109
  13. (with A. R. Schep) Norms of positive operators on Lp-spaces Proc. Amer. Math. Soc. 109 (1990) pp. 135-146
  14. (with P. R. Goodey) Processes of flats induced by higher-dimensional flats II Contemporary Mathematics 113 (1990) pp. 111-119
  15. (with M. A. Sutton, J. R. Dickerson, S. R. McNeil) A constrained, least squares approach for hybrid stress analysis of elastic bodies Engineering Analysis with Boundary Elements 8 (1991)
  16. (with M. L. Reese) Characterization of eigenfunctions by boundedness conditions Canadian Mathematical Bulletin 35 (1992) pp. 204-213
  17. (with A. Treibergs) A reverse isoperimetric inequality, stability and extremal theorems for plane curves with bounded curvature Rocky Mountain Jour. Math., 25 (1995), pp. 635-684.
  18. (with P. R. Goodey and M. Reeder) Processes of Flats Induced by Higher Dimensional Process III Geom. Dedicata, 61 pp. 257-269, (1996)
  19. (with L. Andersson and M. Dahl) Boundary and Lens Rigidity of Lorentzian Surfaces Trans. Amer. Math. Soc., 348 (1996) pp. 2307-2329
  20. (with Paul Sisson) Capturing the Origin with Random Points: Generalizations of a Putnam Problem College Math. Jour., 27 (1996) pp. 186-192
  21. The Sharp Sobolev Inequality and the Banchoff-Pohl Inequality on Surfaces Proc. of the Amer. Math. Soc. 126 (1998) pp. 2779-2787
  22. (with Lars Andersson and Greg Galloway) A Strong Maximum Principle for Weak Solutions of Quasi-Linear Elliptic Equations with Applications to Lorentzian and Riemannian Geometry Comm. Pure Appl. Math., 51 (1998) pp. 581-624.
  23. (with Lars Andersson and Greg Galloway) The Cosmological Time Function Classical and Quantum Gravity 15 (1998) pp. 309-322
  24. (With Lars Andersson) Comparison and rigidity theorems in semi-Riemannian geometry Communications in Analysis and Geometry, 6 (1998) pp. 819-877.
  25. (With S. J. Dilworth and J. W. Roberts) Extremal Approximately Convex Functions and Estimating the Size of Convex Hulls Advances in Mathematics 148 (1999) pp. 1-43.
  26. Blaschke's Rolling Theorem for Manifolds with Boundary Manuscripta Mathematica, 99 (1999) pp. 471-483.
  27. (With Steve Dilworth and Jim Roberts) On the Size of Approximately Convex Sets in Normed Spaces. Studia Mathematica 140 (2000) pp. 213-241.
  28. (With Gyula Károlyi and László A. Székely) Towards a Katona Type Proof for the 2-Intersecting Erdös-Ko-Rado Theorem. Electronic Journal of Combinatorics 8 (2001) R31
  29. (with Piotr T. Chrusciel, Erwann Delay, and Greg Galloway) Regularity of Horizons and the Area Theorem. Annales Henri Poincaré 2 (2001) pp. 109-178.
  30. (with Emil Cornea and Per-Gunnar Martinsson) Solutions Near Singular Points to the Eikonal and Related First Order Non-linear Partial Differential Equations in Two Independent Variables. Differential and Integral Equations, 14 (2001) pp. 1441-1468.
  31. (With S. J. Dilworth and J. W. Roberts) Extremal Approximately Convex Functions and the Best Constants in a Theorem of Hyers and Ulam. Advances in Mathematics 172 (2002) pp. 1-14.
  32. (with Piotr T. Chrusciel, Joe Fu, and Greg Galloway) On fine Differentiability Properties of Horizons and Applications to Riemannian Geometry. Journal of Geometry and Physics 41 (2002) pp. 1-12.
  33. (with Aaron Abrams, Jason Cantarella, Joe Fu, and Mohammad Ghomi) Circles Minimize most Knot Energies. Topology 42 (2003) pp. 381-394.
  34. (with Wenxiong Chen, Erwin Lutwak, Deane Yang, and Gaoyong Zhang) A Generalized Affine Isoperimetric Inequality. J. Geom. Anal. 14 (2004), 597-612.
  35. Constructing Complete Projectively Flat Connections. Rocky Mountain Journal of Mathematics 35 (2005) pp. 1909-1922.
  36. (with S. J. Dilworth and J. W. Roberts) A General Theory of Almost Convex Functions. Transactions of the American Mathematical Society 358 (2006) pp. 3413-3445.
  37. Convex Bodies of Constant Width and Constant Brightness. Advances in Mathematics 204 (2006) pp. 241-261.
  38. (with Daniel Hug) Smooth Convex Bodies with Proportional Projection Functions. To appear in Israel Journal of Mathematics.
  39. (with Daniel Hug) Nakajima's Problem: Convex Bodies of Constant Width and Constant Brightness. To appear in Mathematika.