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On a local solution of the 8th Busemann-Petty problem Alfonseca-Cubero, Maria de los Angeles
Description
The eighth Busemann-Petty problem asks the following question: If for an origin-symmetric convex body $K\subset{\mathbb R^n}$, $n \geq 3$, we have \[ f_K(\theta)=C(vol_{n-1}(K\cap \theta^{\perp}))^{n+1}\qquad\forall \theta\in S^{n-1}, \] where the constant $C$ is independent of $\theta$, must $K$ be an ellipsoid Here, $f_K$ is the is the curvature function (the reciprocal of the Gaussian curvature). We will show that the answer is affirmative for $K$ close enough to the Euclidean ball in the Banach-Mazur distance.
Item Metadata
Title |
On a local solution of the 8th Busemann-Petty problem
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2020-02-12T10:42
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Description |
The eighth Busemann-Petty problem asks the following question:
If for an origin-symmetric convex body $K\subset{\mathbb R^n}$, $n \geq 3$, we have
\[
f_K(\theta)=C(vol_{n-1}(K\cap \theta^{\perp}))^{n+1}\qquad\forall \theta\in S^{n-1},
\]
where the constant $C$ is independent of $\theta$, must $K$ be an ellipsoid
Here, $f_K$ is the is the curvature function (the reciprocal of the Gaussian curvature).
We will show that the answer is affirmative for $K$ close enough to the Euclidean ball in the Banach-Mazur distance.
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Extent |
30.0 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: North Dakota State University
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Series | |
Date Available |
2020-08-11
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0392687
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International