Optimal constant in an L^2 extension problem and a proof of a conjecture of Ohsawa

Abstract

In this paper, we solve the optimal constant problem in the setting of Ohsawa's generalized $L^2$ extension theorem. As applications, we prove a conjecture of Ohsawa and the extended Suita conjecture, we also establish some relations between Bergman kernel and logarithmic capacity on compact and open Riemann surfaces.

arXiv commentThis work was complete in Nov. 2012, Published on line in SCIENCE CHINA Mathematics (2014)

References in corpus (3)

• Invariance of Plurigenera
• Some recent transcendental techniques in algebraic and complex geometry
• Some results related to group actions in several complex variables

Cited by in corpus (13)

• Effectiveness of Demailly's strong openness conjecture and related problems
• Strong openness of multiplier ideal sheaves and optimal $L^2$ extension
• New characterizations of plurisubharmonic functions and positivity of direct image sheaves
• Optimal $L^2$ extension of sections from subvarieties in weakly pseudoconvex manifolds
• A sharp effectiveness result of Demailly's strong openness conjecture
• Concavity property of minimal $L^2$ integrals with Lebesgue measurable gain V--fibrations over open Riemann surfaces
• Extension of cohomology classes and holomorphic sections defined on subvarieties
• Concavity of minimal $L^2$ integrals related to multipler ideal sheaves
• General concavity of minimal $L^2$ integrals related to multiplier ideal sheaves
• Estimation of weighted $L^2$ norm related to Demailly's Strong Openness Conjecture
• Lelong numbers, complex singularity exponents, and Siu's semicontinuity theorem
• Multiplier ideal sheaves, complex singularity exponents, and restriction formula
• A support function of the weighted $L^2$ integrations on the superlevel sets of the weights