Heat dispersion laws in smooth compact manifolds

TL;DR

This paper introduces a new heat dispersion law for Lipschitz conductors in smooth compact Riemannian manifolds, supported by theoretical theorems and propositions.

Contribution

It establishes a novel heat dispersion law and explores its properties through comparison and recycling laws in geometric analysis.

Findings

Newly-established heat dispersion law for Lipschitz conductors.

Comparison law for generic heat dispersion.

Recycling law for quasilinear Laplace-Robin eigenvalues.

Abstract

Given a Lipschitz conductor $K$ in the smooth compact Riemannian $2\le n$-manifold $(M,g)$, such a half generic heat dispersion law $$ {\rm H^d}_{p,\varPhi,\varPsi}(K,M)=2^{-1} {\rm H^d}_{\Delta_p,\varPhi,\varPsi}(K,M) $$ is not only newly-established via Theorem 1.1 but also deeply-explored through not only Proposition 3.1 (a comparison law for the generic heat dispersion) but also Proposition 3.2 (a recycling law for the quasilinear Laplace-Robin eigenvalue).