https://neckpinch.com/authors/jacob-sturm/New arXiv papers by Jacob Sturm, from Neckpinch Tue, 03 Nov 2026 08:37:45 GMT https://neckpinch.com/papers/2209.09428/arxiv:2209.09428Tue, 20 Sep 2022 00:00:00 GMTBin Guo, Duong H. Phong, Jian Song, Jacob Sturm — Diameter estimates for Kähler metrics are established which require only an entropy bound and no lower bound on the Ricci curvature. The proof builds on recent PDE techniques for L^∞ estimates for the Monge-Ampère equation, with a key improvement allowing degeneracies of the volume form of codimension strictly greater than one. As a consequence, diameter bounds are obtained for long-time solutions of the Kähler-Ricci flow and finite-time solutions when the limiting class is big, as well as for special fibrations of Calabi-Yau manifolds.Ricci flowKähler–Ricci flowRicci-flat & Calabi–YauSingularitiesKähler geometryLong-time existence & convergence https://neckpinch.com/papers/2208.03724/arxiv:2208.03724Sun, 07 Aug 2022 00:00:00 GMTKing Leung Lee, Jacob Sturm, Xiaowei Wang — The moment map μ is a central concept in the study of Hamiltonian actions of compact Lie groups K on symplectic manifolds. In this short note, we propose a theory of moment maps coupled with an Ad_K-invariant convex function f on k^(∗), the dual of Lie algebra of K, and study the properties of the critical point of f∘μ. Our motivation comes from Donaldson which is an example of infinite dimensional version of our setting. As an application, we interpret Kähler-Ricci solitons as a special case of the generalized extremal metric.Ricci solitonsKähler–Ricci solitonsKähler geometryHomogeneous spacesKähler–Einstein & K-stability