Fenchel-Willmore-Chen inequality under Lower bounds on weighted intermediate Ricci curvature

In this talk, I will present a weighted version of the Fenchel–Willmore–Chen inequality for closed submanifolds in complete noncompact smooth metric measure spaces. Our result recovers several known inequalities and provides a unified proof. I will explain the main ideas of the proof, based on comparison estimates for the normal exponential map and a Riccati-type inequality. If time permits, I will also discuss an isoperimetric inequality under nonnegative \(1\)-weighted Ricci curvature.

This is a joint work with Guofang Wei.