Heat dispersion laws in smooth compact manifolds

Abstract

Given a Lipschitz conductor $K$ in the smooth compact Riemannian $2\le n$-manifold $(M,g)$, such a half generic heat dispersion law $${{\mathrm{H}}^{\mathrm{d}}}_{p,\Phi ,\Psi }(K,M)=2^{-1}{{\mathrm{H}}^{\mathrm{d}}}_{\hat{I}{”}_p,\Phi ,\Psi }(K,M)$$ 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).