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OP-11432Status unassessedGeometry and topology

Convexity of the Regular Set

PDE methods in complex geometry · AIMPL workshop record

MSC 32 · Several complex variables and analytic spaces

Editorial mapping of AIMPL list topic: PDE methods in complex geometry. http://aimpl.org/pdecomplexgeom/ Not an author-supplied MSC code.

Workshop record · status unassessedAs of 2026-09-10 source snapshot; not a current-status certificationSource & evidence ↓
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Problem statement

Is the regular set of a singular Kahler-Einstein manifold (X,ωKE)(X,\omega_{KE}) convex? That is, is it true that for any two points x,y∈Xregx,y\in X_{\text{reg}}, there is a minimal geodesic in XX from xx to yy which lies entirely in XregX_{\text{reg}}? This is known to be true if XX is a Gromov-Hausdorff limit of a sequence of noncollapsed Kahler-Einstein manifolds by Colding-Naber, and more generally if XX is an RCD space.

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References
  1. [1]PDE methods in complex geometry · Original question link
  2. [2]AIMPL source bibliography link
  3. [3]AIMPL text license · CC BY-SA 3.0 linkAIM Problem Lists (AIMPL), original contributors; CC BY-SA 3.0. Adaptation: structural TeX converted to Markdown, documented source macros expanded, and source bibliography links added. Mathematical wording retained. These adapted source texts remain under CC BY-SA 3.0.

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