A note on the $M^*$--limiting convolution body

Antonis Tsolomitis

A note on the $M^*$--limiting convolution body

度量几何 2016-09-06 v1 泛函分析

作者: Antonis Tsolomitis

摘要

We introduce the mixed convolution bodies of two convex symmetric bodies. We prove that if the boundary of a body $K$ is smooth enough then as $\delta$ tends to $1$ the $\delta$ -- $M^*$ --convolution body of $K$ with itself tends to a multiple of the Euclidean ball after proper normalization. On the other hand we show that the $\delta$ -- $M^*$ --convolution body of the $n$ --dimensional cube is homothetic to the unit ball of $\ell_1^n$ .

关键词

convex bodies convex geometry n-body problem

引用

@article{arxiv.math/9605217,
  title  = {A note on the $M^*$--limiting convolution body},
  author = {Antonis Tsolomitis},
  journal= {arXiv preprint arXiv:math/9605217},
  year   = {2016}
}

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