Rigidity theorems by the logarithmic capacity
Robert Xin Dong, Yuan Zhang
TL;DR
This paper investigates rigidity phenomena linking the Bergman kernel, logarithmic capacity, Green's function, and geometric measures, inspired by the Suita conjecture, revealing new insights into complex analysis and potential theory.
Contribution
It introduces novel rigidity theorems connecting these complex analysis concepts, expanding understanding beyond previous results related to the Suita conjecture.
Findings
Established new rigidity relations involving the Bergman kernel and logarithmic capacity.
Connected Green's function properties with Euclidean geometric measures.
Extended the scope of the Suita conjecture to broader contexts.
Abstract
In light of the Suita conjecture, we explore various rigidity phenomena concerning the Bergman kernel, logarithmic capacity, Green's function, and Euclidean distance and volume.
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Taxonomy
TopicsHolomorphic and Operator Theory · Meromorphic and Entire Functions · Algebraic and Geometric Analysis