Symmetry and compact embeddings for critical exponents in metric-measure spaces

2020/01/31 by Gaczkowski, M., Górka, P., Pons, D. J.
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2002.00076

Abstract

We obtain a compact Sobolev embedding for H-invariant functions in compact metric-measure spaces, where H is a subgroup of the measure preserving bijections. In Riemannian manifolds, H is a subgroup of the volume preserving diffeomorphisms: a compact embedding for the critical exponents follows. The results can be viewed as an extension of Sobolev embeddings of functions invariant under isometries in compact manifolds.

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