Boundary behavior of conformal deformations

Nieminen, Tomi; Tossavainen, Timo

doi:10.1090/S1088-4173-07-00161-0

Boundary behavior of conformal deformations
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by Tomi Nieminen and Timo Tossavainen PDF

Conform. Geom. Dyn. 11 (2007), 56-64 Request permission

Abstract:

We study conformal deformations of the Euclidean metric in the unit ball $\mathbb {B}^{n}$. We assume that the density associated with the deformation satisfies a Harnack inequality and an arbitrary volume growth condition on the isodiametric profile. We establish a Hausdorff (gauge) dimension estimate for the set $E\subset \partial \mathbb {B}^{n}$ where such a deformation mapping can “blow up”. We also prove a generalization of Gerasch’s theorem in our setting.

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