“Convexity of the Mabuchi K-energy and applications.”<\/p>\n
The Mabuchi K-energy is a functional defined on the space of all Kahler metrics in a given cohomology class. A crucial property of the K-energy is that its critical points are metrics of constant scalar curvature. It has been known for a long time that the K-energy is convex along smooth geodesics. This fact is very important as a motivational guide, but its practical usefulness is limited since points in the space cannot be joined by a smooth geodesic. We will prove that the K-energy is in fact also convex along generalized geodesics and discuss applications of this to uniqueness problems. (This is joint work with Robert Berman.)\n<\/p>\n
“Rationally connected manifolds and semipositivity of the Ricci curvature.”<\/p>\n
The talk will explain a structure theorem for compact Kähler manifolds with semipositive anticanonical bundle. Up to finite étale cover, it is shown that such manifolds split holomorphically and isometrically as a product of Ricci flat varieties and of rationally connected manifolds. The proof is based on a characterization of rationally connected manifolds through the
\nnon-existence of certain twisted contravariant tensor products of the tangent bundle, along with a generalized holonomy principle for pseudoeffective line bundles. A crucial ingredient is the characterization of uniruled nonsingular varieties by the property that the anticanonical bundle is not pseudoeffective (this is joint work with Frédéric Campana and Thomas Peternell).<\/p>\n
“Homogeneous Monge-Ampere equations and canonical tubular neighbourhoods in Kahler geoemtry”<\/p>\n
In this talk I will describe some joint work with Julius Ross. By solving the Homogeneous Monge-Ampere equation on the deformation to the normal cone of a complex submanifold of a Kahler manifold, we get a canonical tubular neighbourhood adapted to both the holomorphic and the symplectic structure. If time permits I will describe an application, namely an optimal regularity result for certain naturally defined plurisubharmonic envelopes.<\/p>\n","protected":false},"excerpt":{"rendered":"
Universit\u00e9 libre de Bruxelles, 13\/05\/2014 Bo Berndtsson “Convexity of the Mabuchi K-energy and applications.” The Mabuchi K-energy is a functional defined on the space of all Kahler metrics in a given cohomology class. A crucial property of the K-energy is that its critical points are metrics of constant scalar curvature. It has been known for […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"class_list":["post-39","page","type-page","status-publish","entry"],"featured_image_src":null,"featured_image_src_square":null,"_links":{"self":[{"href":"https:\/\/geometry.ulb.ac.be\/brussels-london\/wp-json\/wp\/v2\/pages\/39","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/geometry.ulb.ac.be\/brussels-london\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/geometry.ulb.ac.be\/brussels-london\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/geometry.ulb.ac.be\/brussels-london\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/geometry.ulb.ac.be\/brussels-london\/wp-json\/wp\/v2\/comments?post=39"}],"version-history":[{"count":2,"href":"https:\/\/geometry.ulb.ac.be\/brussels-london\/wp-json\/wp\/v2\/pages\/39\/revisions"}],"predecessor-version":[{"id":41,"href":"https:\/\/geometry.ulb.ac.be\/brussels-london\/wp-json\/wp\/v2\/pages\/39\/revisions\/41"}],"wp:attachment":[{"href":"https:\/\/geometry.ulb.ac.be\/brussels-london\/wp-json\/wp\/v2\/media?parent=39"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}