SU\G(𝔸)/K·U

The Bochner Technique and Weighted Curvatures

Peter Petersen, Matthias Wink

Type: Article

Publication Date: 2020-07-09

Citations: 4

DOI: https://doi.org/10.3842/sigma.2020.064

Abstract

In this note we study the Bochner formula on smooth metric measure spaces. We introduce weighted curvature conditions that imply vanishing of all Betti numbers.

Locations

  • Symmetry Integrability and Geometry Methods and Applications - View - PDF
  • eScholarship (California Digital Library) - View - PDF
  • arXiv (Cornell University) - View - PDF
  • DataCite API - View

Similar Works

Action Title Year Authors
+ Integral Curvature Bounds and Betti Numbers 2022 Runze Yu
+ The Bochner Technique 2016 Peter Petersen
+ The Bochner Technique 1998 Peter Petersen
+ PDF Chat New curvature conditions for the Bochner Technique 2020 Peter Petersen
Matthias Wink
+ PDF Chat The Weighted Connection and Sectional Curvature for Manifolds With Density 2018 Lee Kennard
William Wylie
Dmytro Yeroshkin
+ Comparison Geometry for the Bakry-Emery Ricci Tensor 2007 Guofang Wei
William Wylie
+ K. YANO and S. BOCHNER: Curvature and Betti numbers 1954 Werner Fenchel
+ PDF Chat The weighted Sobolev and mean value inequalities 2014 Adriano A. Medeiros
+ PDF Chat Geometric measure theory and manifolds of nonnegative Ricci curvature 1996 Yoe Itokawa
Ryoichi Kobayashi
+ The weighted connection and sectional curvature for manifolds with density 2017 Lee Kennard
William Wylie
Dmytro Yeroshkin
+ The weighted connection and sectional curvature for manifolds with density 2017 Lee Kennard
William Wylie
Dmytro Yeroshkin
+ Metrics and Curvature 2023 Parvaneh Joharinad
Jürgen Jost
+ PDF Chat An elementary method in the study of nonnegative curvature 1979 H. Wu
+ Functionals depending on curvatures and surfaces with curvature measures 1990 Gabriele Anzellotti
+ PDF Chat An estimate of Fréchet distances on surfaces of bounded curvature 1956 Folke Eriksson
+ Height estimates and half-space type theorems in weighted product spaces with nonnegative Bakry–Émery–Ricci curvature 2016 Henrique F. de Lima
Márcio S. Santos
+ PDF Chat On the equivalence of the entropic curvature-dimension condition and Bochner’s inequality on metric measure spaces 2014 Matthias Erbar
Kazumasa Kuwada
Karl-Theodor Sturm
+ The Sharp Sobolev Inequality on Metric Measure Spaces with Lower Ricci Curvature Bounds 2015 Angelo Profeta
+ A volume comparison theorem for characteristic numbers 2020 Daniel Luckhardt
+ Spaces of nonnegative curvature 1993 Detlef Gromoll

Works That Cite This (4)

Action Title Year Authors
+ PDF Chat Remarks on the quadratic orthogonal bisectional curvature 2022 Kyle Broder
+ PDF Chat Rigidity Results with Curvature Conditions from Lichnerowicz Laplacian and Applications 2022 Gunhee Cho
Dung Thac Dung
Tra Quang Huy
+ Eigenvalue estimates on weighted manifolds 2022 Volker Branding
Georges Habib
+ Unification of Maxwell Systems, Einstein, and Dirac Equations in Pseudo-Riemannian Space <I>R<sup>1,3</sup></I> by Clifford Algebra 2024 Алимжан Бабаев

Works Cited by This (7)

Action Title Year Authors
+ PDF Chat Volume comparison theorems without Jacobi fields 2005 Dominique Bakry
Zhongmin Qian
+ PDF Chat Comparison geometry for the Bakry-Emery Ricci tensor 2009 Guofang Wei
William Wylie
+ PDF Chat Some geometric properties of the Bakry-�mery-Ricci tensor 2003 John Lott
+ COMPARISON GEOMETRY FOR THE BAKRY-EMERY 2009 Guofang Wei
William Wylie
+ PDF Chat New curvature conditions for the Bochner Technique 2020 Peter Petersen
Matthias Wink
+ PDF Chat Diffusions hypercontractives 1985 Dominique Bakry
Michel Émery
+ Riemannian Geometry 2016 Peter Petersen