Inverse Mean Curvature Flow and a Minkowski inequality in AdS-Schwarzschild manifold
Date:
In this talk, we'll discuss a paper by Brendle-Hung-Wang that applies a monotonicity formula of inverse mean curvature flow to prove a Minkowski inequality in AdS-Schwarzschild manifolds. Despite the lack of full convergence in this context (IMCF on Asymptotically hyperbolic manifold), we establish a roundedness estimate that helps estimate the lower bound of a monotone quantity along the flow. Besides IMCF, Professor Brendle's geometric inequality and a sharp Sobolev inequality on the standard sphere are key components of the proof. References: [A Minkowski Inequality for Hypersurfaces in the Anti‐de Sitter‐Schwarzschild Manifold](https://onlinelibrary.wiley.com/doi/abs/10.1002/cpa.21556)
