The Caffarelli-Kohn-Nirenberg Inequalities on Metric Measure Spaces

2017/11/13 by Willian Isáo Tokura, Tokura, Willian Isao, Levi Adriano +3
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #31C12 #35R01 #53C21 #53C24 #Advanced Differential Geometry Research #Dermatological and Skeletal Disorders #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.1711.04836

openalex publication_date 2017/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Ricci curvature for metric-measure spaces via optimal transport

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