Open AccessAsymptotic of the Green's Function of a Riemannian Manifold and Ito's Stochastic Integrals
Author(s) -
Paul Malliavin
Publication year - 1974
Publication title -
proceedings of the national academy of sciences of the united states of america
Language(s) - English
Resource type - Journals
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.71.2.381
Subject(s) - manifold (fluid mechanics) , riemannian manifold , function (biology) , heat flow , ordinary differential equation , flow (mathematics) , real line , mathematics , heat equation , mathematical analysis , line (geometry) , differential (mechanical device) , differential equation , physics , thermodynamics , geometry , mechanical engineering , evolutionary biology , thermal , engineering , biology
Quantitative estimates are obtained by comparison with ordinary differential equations associated to a subharmonic exhaustion functionq . We associate withq a ratioa , which can be considered as the heat flow in an intrinsic time, and the sup and the inf ofa , namelya + anda - , on the level hypersurfaces ofq . Thena + anda - define heat flows on the real line. Comparison between the heat flow on the manifold and heat flows on the line are obtained by stochastic integrals.