3 papers
math.DG2025
Convexity of the K-energy and Uniqueness of Extremal metrics -- An Expository Introduction
Robert J. Berman, Bo Berndtsson
This article is an expository introduction to our paper Convexity of the K-energy and Uniqueness of Extremal metrics. We present the main ideas behind the proof that Mabuchi's K-en…
math.DG2025
Kähler-Einstein metrics arising from micro-canonical measures and Hamiltonian dynamics
Robert J. Berman
We introduce new probabilistic and variational constructions of (twisted) Kähler-Einstein metrics on complex projective algebraic varieties, drawing inspiration from Onsager's sta…
math.DG2024
Reverse Hölder inequalities on the space of Kähler metrics of a Fano variety and effective openness
Robert J. Berman
A reverse Hölder inequality is established on the space of Kähler metrics in the first Chern class of a Fano manifold X endowed with Darvas L^{p}-Finsler metrics. The inequality…