Isoperimetric inequality, finite total Q-curvature and quasiconformal map

2010/04/02 by Yi Wang, Wang, Yi
Mathematics · #53A30 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53A30

paper · pdf · doi:10.48550/arxiv.1004.0271

24 pages, 1 figure

arxiv created 2010/04/02 · arxiv updated 2010/04/05

Abstract

In this paper, we obtain the isoperimetric inequality on conformally flat manifold with finite total Q-curvature. This is a higher dimensional analogue of Li and Tam's result \citeL-T on surfaces with finite total Gaussian curvature. The main step in the proof is based on the construction of a quasiconformal map whose Jacobian is suitably bounded.

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