Surveys in Differential Geometry

Volume 9 (2004)

Analysis of the cut locus via heat kernel

Pages: 337 – 349



R. Neel (Harvard University)

D. Strook (Massachusetts Institute of Technology)


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.

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