3 papers
math.DG2026
Quantitative Volume Estimate on Singular Sets of One-phase Free Boundary Problems in Ricci Limit Spaces
Alejandro Bellati, Kai-Hsiang Wang
We study limit solutions of the one-phase free boundary problem on noncollapsed Ricci limit spaces. We introduce a quantitative stratification of th…
math.DG2026
Instability of the Fundamental Group for Ricci-Flat Kähler 4-Manifolds
Alejandro Bellati, Ignacio Bustamante
We show that the fundamental group is not locally stable under non-collapsed Gromov--Hausdorff convergence, even among closed Ricci-flat Kähler four-manifolds. More precisely, we c…
math.DG2023
Towards Long-time Geometrization: Stability of the Double-Cusp Spacetimes Under T2-Symmetry
Alejandro Bellati, Martin Reiris
Since the early years of General Relativity, understanding the long-time behavior of the cosmological solutions of Einstein's vacuum equations has been a fundamental yet challengin…