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4 papers · 2 filters
The Poisson equation on complete manifolds with positive spectrum and applications
Ovidiu Munteanu, Natasa Sesum
In this paper we investigate the existence of a solution to the Poisson equation on complete manifolds with positive spectrum and Ricci curvature bounded from below. We show that i…
Differential Harnack Estimates for Time-dependent Heat Equations with Potentials
Xiaodong Cao, Richard S. Hamilton
In this paper, we prove a differential Harnack inequality for positive solutions of time-dependent heat equations with potentials. We also prove a gradient estimate for the positiv…
The harmonic mean curvature flow of nonconvex surfaces in
Panagiota Daskalopoulos, Natasa Sesum
We consider a compact, star-shaped, mean convex hypersurface . We prove that in some cases the flow exists until it shrinks to a point in a spherical manne…
Hamiltonian stationary cones and self-similar solutions in higher dimension
Yng-Ing Lee, Mu-Tao Wang
In [LW], we construct examples of two-dimensional Hamiltonian stationary self-shrinkers and self-expanders for Lagrangian mean curvature flows, which are asymptotic to the union of…