Convexity of Hessian integrals and Poincaré type inequalities

DOI10.1090/S0002-9939-10-10262-7zbMath1192.58015arXiv0905.1640MaRDI QIDQ3566674

Zuoliang Hou

Publication date: 8 June 2010

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0905.1640

zbMATH Keywords

energy functionalcomplex Hessian

Mathematics Subject Classification ID

Functional inequalities, including subadditivity, convexity, etc. (39B62) Inequalities involving derivatives and differential and integral operators (26D10) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items (2)

The Sobolev inequality for complex Hessian equations ⋮ Poincaré- and Sobolev- type inequalities for complex \(m\)-Hessian equations

Cites Work

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• Variational problems and elliptic Monge-Ampère equations
• A Poincaré type inequality for Hessian integrals
• On the Dirichlet problems for symmetric function equations of the eigenvalues of the complex Hessian
• Hessian measures. III
• Weak solutions to the complex Hessian equation.
• On a real Monge-Ampère functional
• Nonlinear elliptic equations and the complex hessian
• The k-Hessian Equation
• An energy estimate for the complex Monge-Ampère operator
• Notions of convexity

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