Contents Online
Surveys in Differential Geometry
Volume 9 (2004)
Analysis of the cut locus via heat kernel
Pages: 337 – 349
DOI: https://dx.doi.org/10.4310/SDG.2004.v9.n1.a9
Authors
Abstract
We study the Hessian of the logarithm of the heat kernel to see what it says about the cut locus of a point. In particular, we show that the cut locus is the set of points at which this Hessian diverges faster than $t^{-1}$ as $t\searrow0$. In addition, we relate the rate of divergence to the conjugacy and other structural properties.
Published 1 January 2004