Michael–Simon inequalities for $$k$$k-th mean curvatures

@article{Wang2013MichaelSimonIF,
  title={Michael–Simon inequalities for \$\$k\$\$k-th mean curvatures},
  author={Yi Wang},
  journal={Calculus of Variations and Partial Differential Equations},
  year={2013},
  volume={51},
  pages={117-138}
}
  • Yi Wang
  • Published 2013
  • Mathematics
  • Calculus of Variations and Partial Differential Equations
This paper continues the study of Alexandrov–Fenchel inequalities for quermassintegrals for $$k$$k-convex domains. It focuses on the application to the Michael–Simon type inequalities for $$k$$k-curvature operators. The proof uses optimal transport maps as a tool to relate curvature quantities defined on the boundary of a domain. 
Inequalities for quermassintegrals on k-convex domains

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Inequalities for quermassintegrals on k-convex domains
On Aleksandrov-Fenchel Inequalities for k-Convex Domains
Topics in Optimal Transportation
Submanifolds, isoperimetric inequalities and optimal transportation
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