{"id":325,"date":"2011-02-22T21:57:06","date_gmt":"2011-02-22T20:57:06","guid":{"rendered":"http:\/\/users.unimi.it\/mazza\/?p=325"},"modified":"2011-02-22T23:37:43","modified_gmt":"2011-02-22T22:37:43","slug":"seminario-242","status":"publish","type":"post","link":"https:\/\/sites.unimi.it\/mazza\/2011\/02\/22\/seminario-242\/","title":{"rendered":"seminario 24\/2"},"content":{"rendered":"

Il giorno giovedi' 24 Febbraio
ore 14:30 Aula 5<\/p>\n

Il dott. Alexandre Kirilov
(Dipartimento di Matematica ed Informatica, Universit\u00e0 di Cagliari)<\/p>\n

terr\u00e0 un seminario su<\/p>\n

"Global regularity and global solvability for smooth vector fields on S3"<\/p>\n

Abstract:
The main goal of this work is to address \u00a0global properties \u00a0for classes of smooth (non)singular vector fields on \"S3\". It is known that on \"S3\" no \"C^infty\" globally hypoelliptic (GH) and no \"C^infty\" globally solvable (cohomologically free (CF) in the sense of Katok) vector fields exist.<\/p>\n

First we consider classes of vector fields with one or two cycles which are attractors for all other integral curves. We show that the cohomological equation \"Lu=f\", \"fin C^infty (S3)\" has at least one \"C^infty\" solution defined on \"S3\" except the attractors and we can extend the soluion as a weak \"L1\" function near the attractors. Moreover, we describe completely the propagation of singularities of all solutions \"u\". As a particular case, we exhibit explicit vector fields whose integral curves coincied with \u00a0the foliations obtained by transversal intersection of linear holomorphic flows in \"C2\" \u00a0with \"S3\" under nondegeneracy conditions.<\/p>\n

Secondly, for a class of nonsingular vector fields which are invariant on the fibers (two dimensional tori) in “generalized solid tori" foliations of \"S3\", we derive necessary and sufficient conditions for partial \"C^infty\" GH and partial \"C^infty\" GS \u00a0with respect to the fibers. We point out that our construction of solid tori yields novel family of \"2D\" tori shrinking to cycles at the end points, different from the Clifford and Lwoson tori.<\/p>\n

Moreover, the integral curves of the vector field correspond to foliations obtained by intersection of linear holomorphic flows with
degeneracies in the Poincare' domain.<\/p>\n

We provide also results on the global solvability for more general classes of smooth vector fields (admitting also singular points) associated in a natural way to intersection of \u00a0linear \"C\" holomorphic flows and linear \"R2\" actions on \"S3\". In particular, we are able to classify completely the global properties of the cohomological equation \u00a0\"Lu =f\" on \"S3\", provided \"L\" is obtained by foliations of linear holomorphic \"C\" or linear \"R2\" actions.<\/p>\n

[Joint work with A.Bergamasco and T. Gramchev]<\/p>\n","protected":false},"excerpt":{"rendered":"

Il giorno giovedi' 24 Febbraio ore 14:30 Aula 5 Il dott. Alexandre Kirilov (Dipartimento di Matematica ed Informatica, Universit\u00e0 di Cagliari) terr\u00e0 un seminario su "Global regularity and global solvability for smooth vector fields on S3" Abstract: The main goal of this work is to address \u00a0global properties \u00a0for classes of smooth (non)singular vector fields … Leggi tutto “seminario 24\/2”<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[14],"tags":[],"class_list":["post-325","post","type-post","status-publish","format-standard","hentry","category-seminari"],"_links":{"self":[{"href":"https:\/\/sites.unimi.it\/mazza\/wp-json\/wp\/v2\/posts\/325","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.unimi.it\/mazza\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sites.unimi.it\/mazza\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sites.unimi.it\/mazza\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.unimi.it\/mazza\/wp-json\/wp\/v2\/comments?post=325"}],"version-history":[{"count":1,"href":"https:\/\/sites.unimi.it\/mazza\/wp-json\/wp\/v2\/posts\/325\/revisions"}],"predecessor-version":[{"id":326,"href":"https:\/\/sites.unimi.it\/mazza\/wp-json\/wp\/v2\/posts\/325\/revisions\/326"}],"wp:attachment":[{"href":"https:\/\/sites.unimi.it\/mazza\/wp-json\/wp\/v2\/media?parent=325"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sites.unimi.it\/mazza\/wp-json\/wp\/v2\/categories?post=325"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sites.unimi.it\/mazza\/wp-json\/wp\/v2\/tags?post=325"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}