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Semiconcave functions in Alexandrov geometry

Introductory Workshop: Modern Riemannian Geometry January 18, 2016 - January 22, 2016

January 19, 2016 (03:30 PM PST - 04:30 PM PST)
Speaker(s): Vitali Kapovitch (University of Toronto)
Location: MSRI: Simons Auditorium
  • differential geometry

  • Riemannian geometry

  • modern geometry

  • curvature

  • curvature estimates

  • Ricci curvature

  • Ricci curvature lower bounds

  • Alexandrov spaces

  • stratified manifolds

  • nilmanifold

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC



I will talk about semiconcave functions on Alexandrov spaces with curvature bounded below. Semiconcave functions and their gradient flows provide an important technical tool for studying Alexandrov spaces with curvature bounded below. I will discuss basic properties and constructions of semi-concave functions and will talk about applications such as Morse theory on Alexandrov spaces which shows that a finite dimensional Alexandrov spaces are stratified manifolds. I will also discuss other applications such as various nilpotency theorems as well as some open problems.

25098?type=thumb Kapovitch 25.2 KB application/pdf Download
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