By using previous results by A.Pr\'astaro on integral bordism groups of PDE's, and some issues of the companion paper, we characterize in a geometric way local and global solutions of (generalized) Yamabe equations and Ricci-flow equations. We prove that such results help to find natural linear and parallel webs on a large category of PDE's, that are important in order to find regular and singular solutions on such PDE's. In particular, by applying algebraic topologic methods on the Ricci-flow equation we definitively prove that the Poincar\'e conjecture on the $3$-dimensional manifolds is true.
Geometry of PDE's. III(II): Webs on PDE's and integral bordism groups. Applications to Riemannian geometry PDE's / Agarwal, R; Prastaro, Agostino. - In: ADVANCES IN MATHEMATICAL SCIENCES AND APPLICATIONS. - ISSN 1343-4373. - STAMPA. - 1:17(2007), pp. 267-285.
Geometry of PDE's. III(II): Webs on PDE's and integral bordism groups. Applications to Riemannian geometry PDE's
PRASTARO, Agostino
2007
Abstract
By using previous results by A.Pr\'astaro on integral bordism groups of PDE's, and some issues of the companion paper, we characterize in a geometric way local and global solutions of (generalized) Yamabe equations and Ricci-flow equations. We prove that such results help to find natural linear and parallel webs on a large category of PDE's, that are important in order to find regular and singular solutions on such PDE's. In particular, by applying algebraic topologic methods on the Ricci-flow equation we definitively prove that the Poincar\'e conjecture on the $3$-dimensional manifolds is true.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
