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Award ID contains: 2203607

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  1. ; ; (, Mathematische Annalen)
    Abstract The stable reduction theorem says that a family of curves of genus$$g\ge 2$$ g ≥ 2 over a punctured curve can be uniquely completed (after possible base change) by inserting certain stable curves at the punctures. We give a new this result for curves defined over$${\mathbb {C}}$$ C , using the Kähler–Einstein metrics on the fibers to obtain the limiting stable curves at the punctures. 
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  2. ; ; (, Journal für die reine und angewandte Mathematik (Crelles Journal))
    Abstract We construct Kähler–Einstein metrics with negative scalar curvature near an isolated log canonical (non-log terminal) singularity.Such metrics are complete near the singularity if the underlying space has complex dimension 2. We also establish a stability result for Kähler–Einstein metrics near certain types of isolated log canonical singularity. As application, for complex dimension 2 log canonical singularity, we show that any complete Kähler–Einstein metric of negative scalar curvature near an isolated log canonical (non-log terminal) singularity is smoothly asymptotically close to model Kähler–Einstein metrics from hyperbolic geometry. 
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    Full Text Available 
  3. ; ; ; (, Mathematische Zeitschrift)
    Free, publicly-accessible full text available June 1, 2026
  4. ; ; ; (, J. Reine Angew. Math. 820 (2025), 153–165.)
    Accepted Manuscript Full Text Available
  5. ; ; ; (, Geometric and functional analysis)
    Accepted Manuscript Full Text Available
  6. ; (, Analysis & PDE)
    We continue our work on the linear theory for equations with conical singularities. We derive interior Schauder estimates for linear elliptic and parabolic equations with a background Kähler metric of conical singularities along a divisor of simple normal crossings. As an application, we prove the short-time existence of the conical Kähler–Ricci flow with conical singularities along a divisor with simple normal crossings. 
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  7. ; (, Journal für die reine und angewandte Mathematik)
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  8. ; (, Geometric and functional analysis)
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