Hermann Karcher

from Wikipedia, the free encyclopedia
Hermann Karcher (left) with Christian Bär , Bures-sur-Yvette 2007

Hermann Karcher (* 1938 ) is a German mathematician who deals with differential geometry .

Karcher received his doctorate in 1966 under Kurt Leichtweiß at the TU Berlin ( convex curves on two-dimensional Riemann manifolds ). As a post-doctoral student he was at the Courant Institute of Mathematical Sciences of New York University with James J. Stoker . From the 1970s he was a professor at the University of Bonn .

Among other things, he dealt with embedded minimal surfaces , where he found new minimal surfaces with David Hoffman and others in the 1980s and 1990s (such as a spiral surface of gender 1) with Hoffman and Fenshung Wei in 1993 ). He also dealt with symmetric spaces , submanifolds, Riemannian manifolds , polyhedra , submersions and harmonic mappings .

His doctoral students include Konrad Polthier and Uwe Abresch .

Fonts

  • with Konrad Polthier Geometry of Minimal Surfaces , Spectrum of Science, October 1990
  • Embedded minimal surfaces and their Riemann surfaces , Annual Report DMV , Volume 101, 1999, pp. 72–96
  • Globale Riemannsche Geometry , Annual Report DMV, Volume 77, 1975, pp. 66-77, online
  • Remarks on polyhedra with given dihedral angles , Comm. Pure Appl. Math., Vol. 21, 1968, pp. 169-174
  • A geometric classification of curved symmetric spaces and the isoparametric construction of the Cayley plane , Asterisque, No. 163/164, 1989, p. 111
  • Embedded minimal surfaces derived from Scherk's example , Manuscripta Mathematica, Volume 62, 1988, pp. 83-114, online
  • Riemannian comparison constructions , in SS Chern (editor) Global Differential Geometry , Mathematical Association of America 1989, pp. 170-222
  • mit Ernst Heintze A general comparison theorem with application to volume estimates for submanifolds , Ann. Sci. Ecole Normale Superieure, Volume 11, 1978, pp. 451-470
  • with Jürgen Jost Geometric methods for obtaining a priori bounds for harmonic mappings , Manuscripta Mathematica, Volume 40, 1982, SS 27-77, Online
  • Submersions via projections , Geometriae dedicata, Volume 74, 1999, p. 249
  • with Peter Buser Almost flat manifolds , Asterisque, Volume 81, 1981 (theory von Gromow )
  • with David Hoffman Complete embedded minimal surfaces of finite total curvature , in Robert Osserman (editor) Geometry V , Encyclopedia of Mathematical Sciences, Volume 90, Springer Verlag 1997
  • Editor with Stefan Hildebrandt Geometric Analysis and Nonlinear Partial Differential Equations , Springer Verlag, 2003

Web links

Commons : Hermann Karcher (mathematician)  - collection of images, videos and audio files

Individual evidence

  1. ^ Begehr Mathematik in Berlin , Shaker 1998
  2. Hermann Karcher in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / name used
  3. ^ D. Hoffman, H. Karcher, F. Wei The Genus One Helicoid and the Minimal Surfaces that Led to its Discovery in: Karen Uhlenbeck (editor) Global Analysis and Modern Mathematics , Publish and Perish, 1993. Bild von Polthier