排序方式: 共有23条查询结果,搜索用时 15 毫秒
1.
We derive sufficiently sharp local dimension-free estimates for volumes of sublevel sets of analytic functions in the unit
ball of ℂ
n
The research was partially supported by the United States-Israel Binational Science Foundation. 相似文献
2.
We study optimal transportation with the quadratic cost function in geodesic metric spaces satisfying suitable non-branching assumptions. We introduce and study the notions of slope along curves and along geodesics, and we apply the latter to prove suitable generalizations of Brenier’s theorem of existence of optimal maps. 相似文献
3.
Tapio Rajala Karl-Theodor Sturm 《Calculus of Variations and Partial Differential Equations》2014,50(3-4):831-846
We prove that in metric measure spaces where the entropy functional is \(K\) -convex along every Wasserstein geodesic any optimal transport between two absolutely continuous measures with finite second moments lives on a non-branching set of geodesics. As a corollary we obtain that in these spaces there exists only one optimal transport plan between any two absolutely continuous measures with finite second moments and this plan is given by a map. The results are applicable in metric measure spaces having Riemannian Ricci curvature bounded below, and in particular they hold also for Gromov-Hausdorff limits of Riemannian manifolds with Ricci curvature bounded from below by some constant. 相似文献
4.
Kai Rajala 《Mathematische Annalen》2007,339(2):445-460
We study the covering properties of mappings of bounded and exponentially integrable distortion on the unit ball. We extend
the results of Eremenko (Proc Am Math Soc 128:557–560, 2000) by proving Bloch-type theorems for mappings of exponentially
integrable distortion. In the case of mappings of bounded distortion, we formulate and prove Bloch’s theorem in its most natural
form.
Research supported by the Academy of Finland, and by NSF grant DMS 0244421. Part of this research was done when the author
was visiting at the University of Michigan. He wishes to thank the department for hospitality. 相似文献
5.
Esa Järvenpää Maarit Järvenpää Antti Käenmäki Tapio Rajala Sari Rogovin Ville Suomala 《Mathematische Zeitschrift》2010,266(1):83-105
Let X be a metric measure space with an s-regular measure μ. We prove that if A ì X{A\subset X} is r{\varrho} -porous, then dimp(A) £ s-crs{{\rm {dim}_p}(A)\le s-c\varrho^s} where dimp is the packing dimension and c is a positive constant which depends on s and the structure constants of μ. This is an analogue of a well known asymptotically sharp result in Euclidean spaces. We illustrate by an example that the
corresponding result is not valid if μ is a doubling measure. However, in the doubling case we find a fixed N ì X{N\subset X} with μ(N) = 0 such that
dimp(A) £ dimp(X)-c(log\tfrac1r)-1rt{{\rm {dim}_p}(A)\le{\rm {dim}_p}(X)-c(\log \tfrac1\varrho)^{-1}\varrho^t} for all r{\varrho} -porous sets A ì X\ N{A \subset X{\setminus} N} . Here c and t are constants which depend on the structure constant of μ. Finally, we characterize uniformly porous sets in complete s-regular metric spaces in terms of regular sets by verifying that A is uniformly porous if and only if there is t < s and a t-regular set F such that A ì F{A\subset F} . 相似文献
6.
The aim of the present paper is to define a notion of weakly differentiable cochain in the generality of metric measure spaces and to study basic properties of such cochains. Our cochains are (sub)additive functionals on a subspace of chains, and a suitable notion of chains in metric spaces is given by Ambrosio–Kirchheim?s theory of metric currents. The notion of weak differentiability we introduce is in analogy with Heinonen–Koskela?s concept of upper gradients of functions. In one of the main results of our paper, we prove continuity estimates for cochains with p-integrable upper gradient in n-dimensional Lie groups endowed with a left-invariant Finsler metric. Our result generalizes the well-known Morrey–Sobolev inequality for Sobolev functions. Finally, we prove several results relating capacity and modulus to Hausdorff dimension. 相似文献
7.
We establish the basic analytic and geometric properties of quasiregular maps f: ω → X, where ω ? ? n is a domain and X is a generalized n-manifold with a suitably controlled geometry. Generalizing the classical Väisälä and Poletsky inequalities, our main theorem shows that the path family method applies to these maps. 相似文献
8.
Tapio Rajala 《Journal of Functional Analysis》2012,263(4):896-924
We construct geodesics in the Wasserstein space of probability measures along which all the measures have an upper bound on their density that is determined by the densities of the endpoints of the geodesic. Using these geodesics we show that a local Poincaré inequality and the measure contraction property follow from the Ricci curvature bounds defined by Sturm. We also show for a large class of convex functionals that a local Poincaré inequality is implied by the weak displacement convexity of the functional. 相似文献
9.
10.
Pekka Pankka Kai Rajala 《Calculus of Variations and Partial Differential Equations》2011,42(1-2):73-91
We consider extensions of differential fields of mappings and obtain a lower bound for energy of quasiconformal extension fields in terms of the topological degree. We also consider the related minimization problem for the q-harmonic energy, and show that the energy minimizers admit higher integrability. 相似文献