The advanced maximum principle for parabolic systems on manifolds with boundary

TL;DR

This paper extends the advanced maximum principle for parabolic systems from closed manifolds to compact manifolds with boundary, broadening its applicability and generalizing existing theorems like Pulemotov's Hopf type theorem.

Contribution

It generalizes the advanced maximum principle to manifolds with boundary, expanding its scope and applicability in geometric analysis.

Findings

Extended maximum principle to manifolds with boundary

Generalized Pulemotov's Hopf type theorem

Broadened the theoretical framework for parabolic systems

Abstract

In this short note we extend Chow and Lu's advanced maximum principles for parabolic systems on closed manifolds to the case of compact manifolds with boundary, which also generalizes a Hopf type theorem of Pulemotov.