Weyl's law on $RC{D}^{\ast }(K,N)$ metric measure spaces

Abstract

In this paper, we will prove the Weyl's law for the asymptotic formula of Dirichlet eigenvalues on metric measure spaces with generalized Ricci curvature bounded from below.

We add some details and update some remarks and the references. The final version

References in corpus (2)

• Behaviour of the reference measure on $\mathsf{RCD}$ spaces under charts
• Local Li-Yau's estimates on $RC{D}^{\ast }(K,N)$ metric measure spaces

Cited by in corpus (6)

• Local spectral convergence in $RC{D}^{\ast }(K,N)$ spaces
• Weyl's law for singular Riemannian manifolds
• Collapsed Ricci limit spaces as non-collapsed $RCD$ spaces
• On the asymptotic behavior of the dimension of spaces of harmonic functions with polynomial growth
• Harmonic functions with polynomial growth on manifolds with nonnegative Ricci curvature
• An almost rigidity Theorem and its applications to noncompact RCD(0,N) spaces with linear volume growth