Geometric aspects of the Harnack Inequality for a nonlocal heat equation

TL;DR

This paper explores the geometric properties of the Harnack inequality for a fractional heat equation, linking sharp bounds to higher-dimensional circular geometry, and extends previous results in the field.

Contribution

It introduces a novel connection between Harnack bounds and geometric structures in higher dimensions, generalizing earlier findings.

Findings

Established a sharp double-sided Harnack bound for fractional heat equations

Linked Harnack bounds to circular geometry in higher dimensions

Extended previous results to more general settings

Abstract

We establish a connection between a sharp double-sided Harnack bound for positive solutions of a fractional heat equation and the circular geometry in higher dimensions. The present work extends and generalizes the results obtained in the preceding paper.