5 citations · 18 across the 20 of their papers we have counts for
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Second Order Bismut formulae and applications to Neumann semigroups on manifolds
Li-Juan Cheng, Anton Thalmaier, Feng-Yu Wang
Let be a complete connected Riemannian manifold with boundary , and let be the Neumann semigroup generated by where for a -vect…
Hessian estimates for Dirichlet and Neumann eigenfunctions of Laplacian
Li-Juan Cheng, Anton Thalmaier, Feng-Yu Wang
By methods of stochastic analysis on Riemannian manifolds, we develop two approaches to determine an explicit constant for an -dimensional compact manifold with bound…
Bismut-Stroock Hessian formulas and local Hessian estimates for heat semigroups and harmonic functions on Riemannian manifolds
Qin-Qian Chen, Li-Juan Cheng, Anton Thalmaier
In this article, we develop a martingale approach to localized Bismut-type Hessian formulas for heat semigroups on Riemannian manifolds. Our approach extends the Hessian formulas e…
Dimension-free Harnack inequalities for conjugate heat equations and their applications to geometric flows
Li-Juan Cheng, Anton Thalmaier
Let be a differentiable manifold endowed with a family of complete Riemannian metrics evolving under a geometric flow over the time interval . In this article, we…
Functional inequalities on manifolds with non-convex boundary
Li-Juan Cheng, Anton Thalmaier, James Thompson
In this article, new curvature conditions are introduced to establish functional inequalities including gradient estimates, Harnack inequalities and transportation-cost inequalitie…
Evolution systems of measures and semigroup properties on evolving manifolds
Li-Juan Cheng, Anton Thalmaier
An evolving Riemannian manifold consists of a smooth -dimensional manifold , equipped with a geometric flow of complete Riemannian metrics, parametri…
Characterization of pinched Ricci curvature by functional inequalities
Li-Juan Cheng, Anton Thalmaier
In this article, functional inequalities for diffusion semigroups on Riemannian manifolds (possibly with boundary) are established, which are equivalent to pinched Ricci curvature,…
A Probabilistic Approach for Gradient Inequalities on Time-Inhomogeneous Manifolds
Li-Juan Cheng
Gradient inequalities of the Hamilton type and the Li-Yau type for positive solutions to the heat equation are established from a probabilistic viewpoint, which simplifies the proo…
Stochastic Analysis on Path Space over Time-Inhomogeneous Manifolds with Boundary
Lijuan Cheng
Let for a -vector field on a differential manifold with possible boundary , where is the Laplacian induced by a time dependent met…
The radial part of Brownian motion with respect to -distance under Ricci flow
Lijuan Cheng
Let be a family of complete time-depending Riemannian matrics on a manifold which evolves under backwards Ricci flow. The Itô formula is established for the…
Reflecting Diffusion Process on Time-Inhomogeneous Manifolds with Boundary
Li-Juan Cheng, Kun Zhang
Let for a -vector field on a differential manifold with boundary , where is the Laplacian induced by a time dependent metric …
Diffusion semigroup on manifolds with time-dependent metrics
Li-Juan Cheng
Let , on a differential manifold equipped with time-depending complete Riemannian metric , where is the Laplacian induced…