The Caffarelli-Kohn-Nirenberg Inequalities on Metric Measure Spaces (1711.04836v1)

Published 13 Nov 2017 in math.DG

Abstract: In this paper, we prove that if a metric measure space satisfies the volume doubling condition and the Caffarelli-Kohn-Nirenberg inequality with same exponent n(n>1), then it has exactly n-dimensional volume growth. As application, we obtain geometric and topological properties of Alexandrov space, Riemannian manifold and Finsler space which support a Caffarelli-Kohn-Nirenberg inequality.

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