On convexity of the regular set of conical Kahler-Einstein metrics

2014/03/25 by Ved Datar, Ved V. Datar, Datar, Ved V. · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG

paper · pdf · doi:10.48550/arxiv.1403.6219

proof of diameter bound added in section 2, modification of the approximation scheme of cone metrics for λ< 0 in section 2, results are unchanged

openalex publication_date 2014/03/25 · arxiv created 2014/07/04 · arxiv updated 2014/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we prove convexity, in the sense of Colding-Naber, of the regular set of solutions to some complex Monge-Ampere equations with conical singularities along simple normal crossing divisors. In particular, any two points in the regular set can be joined by a smooth minimal geodesic lying entirely in the regular set. We show that as a result, the classical theorems of Myers and Bishop-Gromov extend almost verbatim to this singular setting.

Citations

• Sharp Hölder continuity of tangent cones for spaces with a lower Ricci curvature bound and applications

Cited by

• Gromov-Hausdorff limits of collapsing Calabi-Yau fibrations

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