Geometric inequalities and the hoop conjecture

C. Barrabès; André Gramain; Emmanuel Lesigne; Patricio S. Letelier

doi:10.1088/0264-9381/9/9/001

September 1, 1992Classical and Quantum Gravity

Geometric inequalities and the hoop conjecture

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Key Points

This study aims to prove geometric inequalities related to convex bodies and apply them to analytic models of nonspherical collapse.
Proved geometric inequalities for any convex body concerning perimeter and total mean curvature.
Analyzed analytic models of nonspherical collapse to assess implications on the hoop conjecture.
Identified novel connections between perimeter and mean curvature in convex bodies.
Formulated a more precise version of the hoop conjecture using these geometric relationships.

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Implication

Demonstrates refined geometric relationships in convex bodies, indicating clearer hoop conjecture implications.

Abstract

Geometric inequalities holding for any convex body and connecting the perimeter of plane curves associated with this body to the total mean curvature of its boundary are proved. Their application to some analytic models of nonspherical collapse yields a more precise formulation of the hoop conjecture.

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Cite This Study

Barrabès et al. (1992) studied this question.

synapsesocial.com/papers/6a20772955fc9dbe73780731 https://doi.org/10.1088/0264-9381/9/9/001

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Geometric inequalities and the hoop conjecture

Key Points

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Implication

Abstract

Discussion

Cite This Study

Geometric inequalities and the hoop conjecture

Key Points

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Implication

Abstract

Discussion

Cite This Study

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