Interior Cauchy-Schauder estimates for the heat flow in Carnot-Caratheodory spaces

TL;DR

This paper establishes interior Cauchy-Schauder estimates for heat flow in Carnot-Carathéodory spaces, advancing understanding of regularity properties in sub-Riemannian geometry.

Contribution

It introduces new interior estimates for heat equations in Carnot-Carathéodory spaces under Hormander's condition, extending classical PDE theory.

Findings

Derived interior Cauchy-Schauder estimates for heat flow

Enhanced regularity results in Carnot-Carathéodory spaces

Applicable to systems satisfying Hormander's finite rank condition

Abstract

The purpose of this paper is to establish some basic interior estimates of Cauchy-Schauder type for the heat flow associated with a system of smooth vector fields satisfying Hormander's finite rank condition