ScholarLens Back to search
2023•International Journal of MathematicsRequires access

The second-order gradient estimates for the V-heat kernel and its applications

J. C. Su

Open publisher page 0 citations

Abstract

In this paper, we derive the second-order gradient estimates for the [Formula: see text]-heat kernel on complete Riemannian manifolds with Bakry–Emery Ricci curvature bounded from below. Applying these estimates, we proved that the [Formula: see text]-Riesz transform on a complete manifold with nonnegative [Formula: see text]-Bakry–Emery Ricci curvature is of weak type (1,1).

About this research paper

What this paper is about

In this paper, we derive the second-order gradient estimates for the [Formula: see text]-heat kernel on complete Riemannian manifolds with Bakry–Emery Ricci curvature bounded from below. Applying these estimates, we proved that the [Formula: see text]-Riesz transform on a complete manifold with nonnegative [Formula: see text]-Bakry–Emery Ricci curvature is of weak type (1,1).

Why it matters

A significance statement is not available in the OpenAlex record.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

In this paper, we derive the second-order gradient estimates for the [Formula: see text]-heat kernel on complete Riemannian manifolds with Bakry–Emery Ricci curvature bounded from below. Applying these estimates, we proved that the [Formula: see text]-Riesz transform on a complete manifold with nonnegative [Formula: see text]-Bakry–Emery Ricci curvature is of weak type (1,1).

Key concepts: Mathematics, Ricci curvature, Heat kernel, Bounded function, Riemannian manifold, Order (exchange), Curvature, Pure mathematics

Related papers

Related paper 1Related paper 2
Back to paper searchBrowse research topicsOriginal source
The second-order gradient estimates for the V-heat kernel and its applications — Research Paper | ScholarLens