The Busemann-petty Problem in Hyperbolic and Spherical Spaces
نویسنده
چکیده
The Busemann-Petty problem asks whether origin-symmetric convex bodies in R with smaller central hyperplane sections necessarily have smaller n-dimensional volume. It is known that the answer to this problem is affirmative if n ≤ 4 and negative if n ≥ 5. We study this problem in hyperbolic and spherical spaces.
منابع مشابه
A Solution to the Lower Dimensional Busemann-petty Problem in the Hyperbolic Space
The lower dimensional Busemann-Petty problem asks whether origin symmetric convex bodies in R with smaller volume of all k-dimensional sections necessarily have smaller volume. As proved by Bourgain and Zhang, the answer to this question is negative if k > 3. The problem is still open for k = 2, 3. In this article we formulate and completely solve the lower dimensional Busemann-Petty problem in...
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The classical Busemann-Petty problem (1956) asks, whether origin-symmetric convex bodies in R with smaller hyperplane central sections necessarily have smaller volumes. It is known, that the answer is affirmative if n ≤ 4 and negative if n > 4. The same question can be asked when volumes of hyperplane sections are replaced by other comparison functions having geometric meaning. We give unified ...
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