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OP-11443Status unassessedGeometry and topology

Diameter of Moduli of Kahler-Einstein Metrics of General Type

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

Does the moduli space of Kahler-Einstein manifolds of general type equipped with the Weil-Petersen metric have bounded diameter? It is known that local potentials are continuous up to the boundary. Also, is the pp-Nash entropy of the Weil-Petersen metric bounded (with respect to the Euclidean reference metric)?

This is known to be true for curves. What about with respect to the Hodge metric?

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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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