On the Spectra of a Family of Geometric Operators Evolving with Geometric Flows

Abstract

In this work we generalise various recent results on the evolution and monotonicity of the eigenvalues of certain family of geometric operators under some geometric flows. In an attempt to understand the arising similarities we formulate two conjectures on the monotonicity of the eigenvalues of Schrödinger operators under geometric flows. We also pose three questions which we consider to be of a general interest.

Keywords

Witten-Laplacian / Eigenvalues / Monotonicity of eigenvalues / Ricci flow / Ricci–Bourguignon flow / Yamabe flow / Bochner formula / Reilly formula

Funding

FAPESP