2015/11/15 by Feng Du, Du, Feng, Jing Mao +5
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #35R06 #53C21 #53C60 #58J60 #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.1511.04696
openalex publication_date 2015/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we prove that if a metric measure space satisfies the volume doubling condition and the Gagliardo-Nirenberg inequality with the same exponent n (n≥ 2), then it has exactly the n-dimensional volume growth. Besides, two interesting applications have also been given. The one is that we show that if a complete n-dimensional Finsler manifold of nonnegative n-Ricci curvature satisfies the Gagliardo-Nirenberg inequality with the sharp constant, then its flag curvature is identically zero. The other one is that we give an alternative proof to Mao's main result in [23] for smooth metric measure spaces with nonnegative weighted Ricci curvature.