8 июня 2023 г.

Geometric theory of optimal control


четверг, 16:45


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Kenshiro Tashiro


MCP and geodesic dimension on the $l^p$ Heisenberg group

Аннотация доклада: 

We study the measure contraction property $MCP(0,N)$ and the geodesic dimension on the Heisenberg group with the $l^p$ sub-Finsler metric. We show that if $p$ is in $(2,\infty]$, then it fails to be $MCP(0,N)$. On the other hand, if $p$ is in $(1,2)$, then it satisfies $MCP(0,N)$ with $N$ strictly greater than $2q+1$ (q being the Hölder conjugate). Furthermore, the geodesic dimension is explicitly given by $\min\{2q+2,5\}$ for all $p$ in $[1,\infty)$. When $p$ is in $(1,\infty)$, our technique is based on the Taylor expansion of the generalized trigonometric function. If $p$ is $1$ or infinity, then its branching geodesics and cut locus are explicitly computed and it yields the conclusion.

This is a joint work with Samuel Borza (SISSA). We put the preprint on the following arXiv link.