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Geometry and Nonlinear Partial Differential Equations
Edited by: Vladimir Oliker and Andrejs Treibergs
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Contemporary Mathematics
1992; 154 pp; softcover
Volume: 127
ISBN-10: 0-8218-5135-7
ISBN-13: 978-0-8218-5135-7
List Price: US$44
Member Price: US$35.20
Order Code: CONM/127
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This volume contains the proceedings of an AMS Special Session on Geometry, Physics, and Nonlinear PDEs, held in March 1990 at the AMS meeting in Fayetteville. In recent years, there has been an enormous surge of activity in these areas, and there was an overwhelming response to invitations to the session. The conference brought together specialists in Monge-Ampere equations, prescribed curvature problems, mean curvature, harmonic maps, evolution with curvature-dependent speed, isospectral manifolds, and general relativity. Twenty-five half-hour addresses were presented at the session, and the majority of the papers in this volume are expositions of those addresses. The book provides an excellent overview of the frontiers of research in these areas.

Table of Contents

  • J. K. Beem and P. E. Parker -- Null directions and curvature
  • P. Delanoe -- Generalized stereographic projections with prescribed scalar curvature
  • P. E. Ehrlich and G. G. Emch -- The conjugacy index and simple astigmatic focusing
  • M. E. Gage -- On the size of the blow-up set for a quasilinear parabolic equation
  • S. I. Goldberg and D. Perrone -- Contact \(3\)-manifolds with positive scalar curvature
  • B. Kawohl -- Remarks on the operator div\((\nabla u/|\nabla u|)\)
  • J. M. Lee -- Finite inverse spectral geometry
  • R. C. McOwen -- Conformal metrics with singularities and finite negative total curvature on Riemann surfaces
  • P. Li, A. Treibergs, and S. T. Yau -- How to hear the volume of convex domains
  • N. Uraltseva -- Gradient estimates for solutions of nonlinear parabolic oblique boundary problem
  • S. W. Wei -- Liouville theorems and regularity of minimizing harmonic maps into super-strongly unstable manifolds
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