Exotic heat PDE's

TL;DR

This paper explores exotic heat equations using PDE algebraic topology to characterize global solutions, contributing to the understanding of complex geometric problems like the Poincaré conjecture.

Contribution

It introduces a novel application of PDE algebraic topology to analyze exotic heat equations and their role in solving major geometric conjectures.

Findings

Established a link between exotic heat PDEs and the Poincaré conjecture

Developed a methodology to characterize global solutions of these PDEs

Extended the framework to related geometric problems

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.