Sharp capacity estimates for annuli in weighted R^n and in metric spaces
Björn, A., Björn, J., & Lehrbäck, J. (2017). Sharp capacity estimates for annuli in weighted R^n and in metric spaces. Mathematische Zeitschrift, 286 (3-4), 1173- 1215. doi:10.1007/s00209-016-1797-4
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Mathematische ZeitschriftDate
2017Discipline
MatematiikkaCopyright
© The Author(s) 2016. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License.
We obtain estimates for the nonlinear variational capacity of annuli in weighted Rn
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 Rn. Indeed, to illustrate the sharpness of our estimates, we give
several examples of radially weighted Rn, which are based on quasiconformality of radial
stretchings in Rn.
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Springer Berlin HeidelbergISSN Search the Publication Forum
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Except where otherwise noted, this item's license is described as © The Author(s) 2016. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License.
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