Ellipsoids in pseudoconvex domains
Laszlo Lempert
TL;DR
This paper investigates the problem of finding the largest hermitian ellipsoid that can fit inside a pseudoconvex domain in complex space, establishing existence, uniqueness, and a characterization of the optimal ellipsoid.
Contribution
It introduces a novel approach to inscribed ellipsoids in pseudoconvex domains, proving existence, uniqueness, and providing a characterization of the maximizer.
Findings
Existence of maximal inscribed hermitian ellipsoids in pseudoconvex domains
Uniqueness of the maximal inscribed ellipsoid
Characterization of the maximizer
Abstract
We consider the problem of maximizing the volume of hermitian ellipsoids inscribed in a given pseudoconvex domain in complex Euclidean space. We prove existence and uniqueness, and give a characterization of the maximizer.
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Taxonomy
TopicsHolomorphic and Operator Theory · Analytic and geometric function theory · Geometry and complex manifolds