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pro vyhledávání: '"Schultz, Timo"'
We investigate metric conditions that allow to prove existence and uniqueness of a map solving the Monge problem between two marginals in a metric (measure) space, proving two main results. Firstly, we introduce a nonsmooth version of the Riemannian
Externí odkaz:
http://arxiv.org/abs/2410.22567
Publikováno v:
Calc. Var. Partial Differ. Equ. 63:16 (2024)
We extend the result of Lisini (Calc Var Partial Differ Equ 28:85-120, 2007) on the superposition principle for absolutely continuous curves in $p$-Wasserstein spaces to the special case of $p=1$. In contrast to the case of $p>1$, it is not always po
Externí odkaz:
http://arxiv.org/abs/2209.04268
We prove that on an arbitrary metric measure space a countable collection of test plans is sufficient to recover all $\rm BV$ functions and their total variation measures. In the setting of non-branching ${\sf CD}(K,N)$ spaces (with finite reference
Externí odkaz:
http://arxiv.org/abs/2109.04980
Autor:
Pasqualetto, Enrico, Schultz, Timo
The aim of this paper is to study ultralimits of pointed metric measure spaces (possibly unbounded and having infinite mass). We prove that ultralimits exist under mild assumptions and are consistent with the pointed measured Gromov-Hausdorff converg
Externí odkaz:
http://arxiv.org/abs/2102.11365
Autor:
Schultz, Timo
In this paper, we prove that a metric measure space which has at least one open set isometric to an interval, and for which the (possibly non-unique) optimal transport map exists from any absolutely continuous measure to an arbitrary measure, is a on
Externí odkaz:
http://arxiv.org/abs/1912.01579
Autor:
Schultz, Timo
We show the equivalence of the definitions of very strict $CD(K,N)$ -condition defined, on one hand, using (only) the entropy functionals, and on the other, the full displacement convexity class $\mathcal{DC}_N$. In particular, we show that assuming
Externí odkaz:
http://arxiv.org/abs/1906.07693
Autor:
Rajala, Tapio, Schultz, Timo
We give an alternative proof for the fact that in $n$-dimensional Alexandrov spaces with curvature bounded below there exists a unique optimal transport plan from any purely $(n-1)$-unrectifiable starting measure, and that this plan is induced by an
Externí odkaz:
http://arxiv.org/abs/1803.10023
We show that in a bounded simply connected planar domain $\Omega$ the smooth Sobolev functions $W^{k,\infty}(\Omega)\cap C^\infty(\Omega)$ are dense in the homogeneous Sobolev spaces $L^{k,p}(\Omega)$.
Comment: 17 pages, 4 figures
Comment: 17 pages, 4 figures
Externí odkaz:
http://arxiv.org/abs/1801.02824
Autor:
Schultz, Timo
We introduce a more restrictive version of the strict $CD(K,\infty)$ -condition, the so-called very strict $CD(K,\infty)$ -condition, and show the existence of optimal maps in very strict $CD(K,\infty)$ -spaces despite the possible lack of uniqueness
Externí odkaz:
http://arxiv.org/abs/1712.03670
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