Exotic heat PDE's

zbMATH Open1276.55008arXiv1006.4483MaRDI QIDQ662340

Agostino Prástaro

Publication date: 22 February 2012

Published in: Communications in Mathematical Analysis (Search for Journal in Brave)

Abstract: Exotic heat equations that allow to prove the Poincar'e conjecture, some related problems and suitable generalizations too are considered. The methodology used is the PDE's algebraic topology, introduced by A. Pr'astaro in the geometry of PDE's, in order to characterize global solutions.

Full work available at URL: https://arxiv.org/abs/1006.4483

zbMATH Keywords

conservation lawscrystallographic groupsintegral bordisms in PDE'sexistence of local and global solutions in PDE'sPDE's on complex manifolds categoryPDE's on quantum supermanifolds categorysingular PDE's

Mathematics Subject Classification ID

Characteristic classes and numbers in differential topology (57R20) Bordism and cobordism theories and formal group laws in algebraic topology (55N22) Other geometric groups, including crystallographic groups (20H15) Global theory of complex singularities; cohomological properties (32S20) Boundary value problems on manifolds (58J32) Topological aspects of complex manifolds (32Q55) Analysis on supermanifolds or graded manifolds (58C50) Noncommutative global analysis, noncommutative residues (58J42)

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