L2-estimates on p-convex Riemannian manifolds

TL;DR

This paper develops L2-estimates for the exterior differential operator on p-convex Riemannian manifolds, leading to new results on the vanishing and finiteness of de Rham cohomology groups.

Contribution

It introduces novel L2-estimates tailored for p-convex Riemannian manifolds and applies these to derive cohomological vanishing and finiteness results.

Findings

L2-estimates established for exterior differential operator

Vanishing results for de Rham cohomology groups

Finiteness results for certain cohomology groups

Abstract

In this paper, we establish various L2-estimates for the exterior differential operator on p-convex Riemannian manifolds in the sense of Harvey and Lawson. As geometric applications, we prove vanishing and finiteness results for the de Rham cohomology groups.