Resolvent estimates in Schatten spaces for Laplace-Beltrami operators on compact manifolds

TL;DR

This paper establishes resolvent estimates in Schatten spaces for Laplace-Beltrami operators on compact manifolds at the critical exponent, utilizing known bounds for the Hadamard parametrix.

Contribution

It provides the first resolvent estimates in Schatten spaces at the critical exponent for these operators on compact manifolds.

Findings

Resolvent estimates in Schatten spaces at the critical exponent

Use of Hadamard parametrix bounds in the proof

Applicable to Laplace-Beltrami operators on compact manifolds

Abstract

We prove resolvent estimates in Schatten spaces for Laplace-Beltrami operators on compact manifolds at the critical exponent. Our proof only uses known bounds for the Hadamard parametrix.