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<title><string language="fre"><![CDATA[F. Schulze - Mean curvature flow with generic initial data]]></string></title>
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<string language="fre"><![CDATA[Mean
curvature flow is the gradient flow of the area functional and 
constitutes a natural geometric heat equation on the space of 
hypersurfaces in an ambient Riemannian manifold. It is believed, similar
to Ricci Flow in the intrinsic setting, to have the potential to serve 
as a tool to approach several fundamental conjectures in geometry. The 
obstacle for these applications is that the flow develops singularities,
which one in general might not be able to classify completely. 
Nevertheless, a well-known conjecture of Huisken states that a generic 
mean curvature flow should have only spherical and cylindrical 
singularities. As a first step in this direction Colding-Minicozzi have 
shown in fundamental work that spheres and cylinders are the only 
linearly stable singularity models. As a second step toward Huisken's 
conjecture we show that mean curvature flow of generic initial closed 
surfaces in R^3 avoids asymptotically conical and non-spherical compact 
singularities. The main technical ingredient is a long-time existence 
and uniqueness result for ancient mean curvature flows that lie on one 
side of asymptotically conical or compact self-similarly shrinking 
solutions. This is joint work with Otis Chodosh, Kyeongsu Choi and 
Christos Mantoulidis.]]></string></description>
<keyword><string language="fre"><![CDATA[Grenoble]]></string></keyword><keyword><string language="fre"><![CDATA[eem2021]]></string></keyword><keyword><string language="fre"><![CDATA[contraintes de courbures et espaces métriques]]></string></keyword><keyword><string language="fre"><![CDATA[curvature constraints and spaces of metrics]]></string></keyword><keyword><string language="fre"><![CDATA[mean curvature flow]]></string></keyword><keyword><string language="fre"><![CDATA[generic initial data]]></string></keyword>
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