Tag: convergence

Title: On the Minkowski inequality near the sphere Authors: Otis Chodosh, Michael Eichmair, Thomas Koerber Categories: math.DG Comments: All comments welcome \\ We construct a sequence $\{\Sigma_\ell\}_{\ell=1}^\infty$ of closed, axially symmetric surfaces $\Sigma_\ell\subset \mathbb{R}^3$ that converges to the unit sphere in $W^{2,p}\cap C^1$ for every $p\in[1,\infty)$ and such that, for every $\ell$, $$ \int_{\Sigma_{\ell}}H_{\Sigma_\ell}-\sqrt{16\,\pi\,|\Sigma_{\ell}|}