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Documents  53C44 | enregistrements trouvés : 5

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We will give a survey of recent research progress on ancient or eternal solutions to geometric flows such as the Ricci flow, the Mean Curvature flow and the Yamabe flow.
We will address the classification of ancient solutions to parabolic equations as well as the construction of new ancient solutions from the gluing of two or more solitons.

53C44

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For surfaces immersed into a compact Riemannian manifold, we consider the curvature functional given by the $L^{2}$ integral of the second fundamental form. We discuss an area bound in terms of the energy, with application to the existence of minimizers. This is joint work with V. Bangert.

53C44 ; 53C45

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We discuss singularities of Teichmüller harmonic map flow, which is a geometric flow that changes maps from surfaces into branched minimal immersions, and explain in particular how winding singularities of the map component can lead to singular behaviour of the metric component.

53C44 ; 30F60

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Multi angle  Pluripotential Kähler-Ricci flows
Guedj, Vincent (Auteur de la Conférence) | CIRM (Editeur )

We develop a parabolic pluripotential theory on compact Kähler manifolds, defining and studying weak solutions to degenerate parabolic complex Monge-Ampere equations. We provide a parabolic analogue of the celebrated Bedford-Taylor theory and apply it to the study of the Kähler-Ricci flow on varieties with log terminal singularities.

53C44 ; 32W20 ; 58J35

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By a gluing construction, we produce steady Kähler-Ricci solitons on equivariant crepant resolutions of $\mathbb{C}^n/G$, where $G$ is a finite subgroup of $SU(n)$, generalizing Cao’s construction of such a soliton on a resolution of $\mathbb{C}^n/\mathbb{Z}_n$.
This is joint work with Olivier Biquard.

53C25 ; 53C44 ; 53C55

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