3 papers
math.DG2026
Magnitude of metric measure spaces and integrals over geodesics
Yoshinori Hashimoto
We propose a definition of magnitude for a length space with a Borel measure, which involves integrals over the set of geodesics. This quantity agrees with the magnitude of finite…
math.DG2025
Relative uniform -stability over models implies existence of extremal metrics
Yoshinori Hashimoto
We prove that an extremal metric on a polarised smooth complex projective variety exists if it is -uniformly -stable relative to the extremal torus over models, exte…
math.DG2023
Balanced metrics for extremal Kähler metrics and Fano manifolds
Yoshinori Hashimoto
The first three sections of this paper are a survey of the author's work on balanced metrics and stability notions in algebraic geometry. The last section is devoted to proving the…