Li Ma
Published 2006-04-04, updated 2009-10-14Version 2
In this paper, we study the partial convexity of smooth solutions to the heat equation on a compact or complete non-compact Riemannian manifold M or Kahler-Ricci flow. We show that under a natural assumption, a new partial convexity property for smooth solutions to the heat equation is preserved.
Smooth solutions to the Christoffel problem in $\mathbb{H}^{n+1}$
Sharp gradient estimate and Yau's Liouville theorem for the heat equation on noncompact manifolds
Some gradient estimates for the heat equation on domains and for an equation by Perelman
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