Stability of volume comparison for complex convex bodies
Alexander Koldobsky
TL;DR
This paper establishes a stability result for the Busemann-Petty problem concerning sections of complex convex bodies, confirming the robustness of volume comparison under certain conditions.
Contribution
It provides the first stability proof for the affirmative case of the Busemann-Petty problem in the context of complex convex bodies.
Findings
Proved stability in the affirmative part of the Busemann-Petty problem for complex convex bodies.
Demonstrated volume comparison robustness in complex convex geometry.
Enhanced understanding of volume inequalities in complex convex bodies.
Abstract
We prove stability in the affirmative part of the Busemann-Petty problem on sections of complex convex bodies.
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Taxonomy
TopicsPoint processes and geometric inequalities · Geometric Analysis and Curvature Flows