5 citations · 18 across the 20 of their papers we have counts for
20 papers
Covariant Riesz transform on differential forms for
Li-Juan Cheng, Anton Thalmaier, Feng-Yu Wang
In this paper, we study -boundedness () of the covariant Riesz transform on differential forms for a class of non-compact weighted Riemannian manifolds without assu…
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…
Hessian heat kernel estimates and Calderón-Zygmund inequalities on complete Riemannian manifolds
Jun Cao, Li-Juan Cheng, Anton Thalmaier
We address some fundamental questions concerning geometric analysis on Riemannian manifolds. It has been asked whether the -Calderón-Zygmund inequalities extend to a reasonabl…
Some inequalities on Riemannian manifolds linking Entropy,Fisher information, Stein discrepancy and Wasserstein distance
Li-Juan Cheng, Feng-Yu Wang, Anton Thalmaier
For a complete connected Riemannian manifold let be such that $μ(d x)={\rm e}^{-V(x)} \mbox{vol}(d x)$ is a probability measure on . Taking as reference me…
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…
Exponential contraction in Wasserstein distance on static and evolving manifolds
Li-Juan Cheng, Anton Thalmaier, Shao-Qin Zhang
In this article, exponential contraction in Wasserstein distance for heat semigroups of diffusion processes on Riemannian manifolds is established under curvature conditions where…
Functional inequalities on path space of sub-Riemannian manifolds and applications
Li-Juan Cheng, Erlend Grong, Anton Thalmaier
For sub-Riemannian manifolds with a chosen complement, we first establish the derivative formula and integration by parts formula on path space with respect to a natural gradient o…
Uniform gradient estimates on manifolds with a boundary and applications
Li-Juan Cheng, Anton Thalmaier, James Thompson
We revisit the problem of obtaining uniform gradient estimates for Dirichlet and Neumann heat semigroups on Riemannian manifolds with boundary. As applications, we obtain isoperime…
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…
Quantitative -estimates by Bismut formulae
Li-Juan Cheng, Anton Thalmaier, James Thompson
For a function and an elliptic operator , we prove a quantitative estimate for the derivative in terms of local bounds on and . An integral version of thi…
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 method for gradient estimates of some geometric flows
Xin Chen, Li-Juan Cheng, Jing Mao
In general, gradient estimates are very important and necessary for deriving convergence results in different geometric flows, and most of them are obtained by analytic methods. In…
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…