Li-Yau Multiplier Set and Optimal Li-Yau Gradient Estimate on Hyperbolic Spaces

Li-Yau gradient estimates on closed manifolds under bakry-emery ricci curvature conditions

“…(2.24) From (2.24), a short argument from [28] (see also [26]) implies that the same bound actually holds if one replaces the f -heat kernel by any positive solution of the f -heat equation.…”

“…Moreover, Li-Yau-type bounds were also got for weighted manifolds with Bakry-Émery Ricci curvature bounded below [12]. More information about Li-Yau-type bounds can be found in ( [8], [10], [16], [18], [27], [25], [24], [26]).…”

Matrix Li–Yau–Hamilton estimates under Ricci flow and parabolic frequency

“…Without the nonnegativity of sectional curvatures, we have to estimate the terms involving curvature and derivatives of u and the proof becomes much more involved. Here we employ an idea that has has been used in [ 46 , 69 ], and [ 72 ], namely we first prove the estimate for the heat kernel and then derive the estimate for any positive solution to the heat equation.…”

Superconvexity of the heat kernel on hyperbolic space with applications to mean curvature flow

“…In this short note we use observations from [8] and [11] to prove the following convexity estimate for K n . Theorem 1.1.…”