Isoperimetric Functional Inequalities via the Maximum Principle: The Exterior Differential Systems Approach

  • Paata Ivanisvili
  • Alexander Volberg
Part of the Operator Theory: Advances and Applications book series (OT, volume 261)


Our goal in this note is to give a unified approach to the solutions of a class of isoperimetric problems by relating them to the exterior differential systems studied by R. Bryant and P. Griffiths.


Log-Sobolev inequality Poincaré inequality Bobkov’s inequality Gaussian isoperimetry semigroups maximum principle Monge–Ampère equations exterior differential systems backward heat equation (B) theorem 

Mathematics Subject Classification (2010)

Primary 42B20 Secondary 42B35 47A30 


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsKent State UniversityKentUSA
  2. 2.Department of MathematicsMichigan State UniversityEast LansingUSA

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