Search results for "C65"
showing 10 items of 51 documents
Harmonic morphisms in nonlinear potential theory
1992
This article concerns the following problem: given a family of partial differential operators with similar structure and given a continuous mapping f from an open set Ω in Rn into Rn, then when does f pull back the solutions of one equation in the family to solutions of another equation in that family? This problem is typical in the theory of differential equations when one wants to use a coordinate change to study solutions in a different environment.
Duality of moduli in regular toroidal metric spaces
2020
We generalize a result of Freedman and He [4, Theorem 2.5], concerning the duality of moduli and capacities in solid tori, to sufficiently regular metric spaces. This is a continuation of the work of the author and Rajala [12] on the corresponding duality in condensers. peerReviewed
Sharp capacity estimates for annuli in weighted R^n and in metric spaces
2017
We obtain estimates for the nonlinear variational capacity of annuli in weighted R^n and in metric spaces. We introduce four different (pointwise) exponent sets, show that they all play fundamental roles for capacity estimates, and also demonstrate that whether an end point of an exponent set is attained or not is important. As a consequence of our estimates we obtain, for instance, criteria for points to have zero (resp. positive) capacity. Our discussion holds in rather general metric spaces, including Carnot groups and many manifolds, but it is just as relevant on weighted R^n. Indeed, to illustrate the sharpness of our estimates, we give several examples of radially weighted R^n, which …
Differentiability in the Sobolev space W1,n-1
2014
Let Ω ⊂ Rn be a domain, n ≥ 2. We show that a continuous, open and discrete mapping f ∈ W1,n−1 loc (Ω, Rn ) with integrable inner distortion is differentiable almost everywhere on Ω. As a corollary we get that the branch set of such a mapping has measure zero. peerReviewed
Uniformization with infinitesimally metric measures
2019
We consider extensions of quasiconformal maps and the uniformization theorem to the setting of metric spaces $X$ homeomorphic to $\mathbb R^2$. Given a measure $\mu$ on such a space, we introduce $\mu$-quasiconformal maps $f:X \to \mathbb R^2$, whose definition involves deforming lengths of curves by $\mu$. We show that if $\mu$ is an infinitesimally metric measure, i.e., it satisfies an infinitesimal version of the metric doubling measure condition of David and Semmes, then such a $\mu$-quasiconformal map exists. We apply this result to give a characterization of the metric spaces admitting an infinitesimally quasisymmetric parametrization.
Generalized John disks
2014
Abstract We establish the basic properties of the class of generalized simply connected John domains.
Convergence for varying measures
2023
Some limit theorems of the type $\int_{\Omega}f_n dm_n -- --> \int_{\Omega}f dm$ are presented for scalar, (vector), (multi)-valued sequences of m_n-integrable functions f_n. The convergences obtained, in the vector and multivalued settings, are in the weak or in the strong sense.
Three viewpoints on the integral geometry of foliations
1999
We deal with three different problems of the multidimensional integral geometry of foliations. First, we establish asymptotic formulas for integrals of powers of curvature of foliations obtained by intersecting a foliation by affine planes. Then we prove an integral formula for surfaces of contact of an affine hyperplane with a foliation. Finally, we obtain a conformally invariant integral-geometric formula for a foliation in three-dimensional space.
Multi-integrals of finite variation
2020
The aim of this paper is to investigate different types of multi-integrals of finite variation and to obtain decomposition results.
A Newman property for BLD-mappings
2019
We define a Newman property for BLD-mappings and prove that for a BLD-mapping between generalized manifolds equipped with complete path-metrics, this property is equivalent to the branch set being porous when the codomain is LLC. peerReviewed