Functional inequalities and manifolds with nonnegative weighted Ricci curvature

Jing Mao

Czechoslovak Mathematical Journal (2020)

  • Volume: 70, Issue: 1, page 213-233
  • ISSN: 0011-4642

Abstract

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We show that n -dimensional ( n ⩾ 2 ) complete and noncompact metric measure spaces with nonnegative weighted Ricci curvature in which some Caffarelli-Kohn-Nirenberg type inequality holds are isometric to the model metric measure n -space (i.e. the Euclidean metric n -space). We also show that the Euclidean metric spaces are the only complete and noncompact metric measure spaces of nonnegative weighted Ricci curvature satisfying some prescribed Sobolev type inequality.

How to cite

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Mao, Jing. "Functional inequalities and manifolds with nonnegative weighted Ricci curvature." Czechoslovak Mathematical Journal 70.1 (2020): 213-233. <http://eudml.org/doc/297284>.

@article{Mao2020,
abstract = {We show that $n$-dimensional $(n\geqslant 2)$ complete and noncompact metric measure spaces with nonnegative weighted Ricci curvature in which some Caffarelli-Kohn-Nirenberg type inequality holds are isometric to the model metric measure $n$-space (i.e. the Euclidean metric $n$-space). We also show that the Euclidean metric spaces are the only complete and noncompact metric measure spaces of nonnegative weighted Ricci curvature satisfying some prescribed Sobolev type inequality.},
author = {Mao, Jing},
journal = {Czechoslovak Mathematical Journal},
keywords = {Caffarelli-Kohn-Nirenberg type inequality; weighted Ricci curvature; volume comparison},
language = {eng},
number = {1},
pages = {213-233},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Functional inequalities and manifolds with nonnegative weighted Ricci curvature},
url = {http://eudml.org/doc/297284},
volume = {70},
year = {2020},
}

TY - JOUR
AU - Mao, Jing
TI - Functional inequalities and manifolds with nonnegative weighted Ricci curvature
JO - Czechoslovak Mathematical Journal
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 70
IS - 1
SP - 213
EP - 233
AB - We show that $n$-dimensional $(n\geqslant 2)$ complete and noncompact metric measure spaces with nonnegative weighted Ricci curvature in which some Caffarelli-Kohn-Nirenberg type inequality holds are isometric to the model metric measure $n$-space (i.e. the Euclidean metric $n$-space). We also show that the Euclidean metric spaces are the only complete and noncompact metric measure spaces of nonnegative weighted Ricci curvature satisfying some prescribed Sobolev type inequality.
LA - eng
KW - Caffarelli-Kohn-Nirenberg type inequality; weighted Ricci curvature; volume comparison
UR - http://eudml.org/doc/297284
ER -

References

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