Robert Haslhofer - The moduli space of 2-convex embedded spheres
- document 1 document 2 document 3
- niveau 1 niveau 2 niveau 3
- audio 1 audio 2 audio 3
Descriptif
We investigate the topology of the space of smoothly embedded n-spheres in R^{n+1}, i.e. the quotient space M_n:=Emb(S^n,R^{n+1})/Diff(S^n). By Hatcher’s proof of the Smale conjecture, M_2 is contractible. This is a highly nontrivial theorem generalizing in particular the Schoenflies theorem and Cerf’s theorem.In this talk, I will explain how geometric analysis can be used to study the topology of M_n respectively some of its variants.I will start by sketching a proof of Smale’s theorem that M_1 is contractible. By a beautiful theorem of Grayson, the curve shortening flow deforms any closed embedded curve in the plane to a round circle, and thus gives a geometric analytic proof of the fact that M_1 is path-connected. By flowing, roughly speaking, all curves simultaneously, one can improve path-connectedness to contractibility.In the second half of my talk, I’ll describe recent work on space of smoothly embedded spheres in the 2-convex case, i.e. when the sum of the two smallest principal curvatures is positive. Our main theorem (joint with Buzano and Hershkovits) proves that this space is path-connected, for every n. The proof uses mean curvature flow with surgery.
Notice
Dans la même collection
-
Robert Young - Quantitative rectifiability and differentiation in the Heisenberg groupYoungRobert Kehoe.
(joint work with Assaf Naor) The Heisenberg group $\mathbb{H}$ is a sub-Riemannian manifold that is unusually difficult to embed in $\mathbb{R}^n$. Cheeger and Kleiner introduced a new notion of
-
Vincent Beffara - Percolation of random nodal linesBeffaraVincent
Percolation of random nodal lines
-
Melanie Rupflin - Horizontal curves of metrics and applications to geometric flowsRupflinMelanie
On closed surfaces there are three basic ways to evolve a metric, by conformal change, by pull-back with diffeomorphisms and by horizontal curves, moving orthogonally to the first two types of
-
Jeff Viaclovsky - Deformation theory of scalar-flat Kahler ALE surfacesViaclovskyJeff
I will discuss a Kuranishi-type theorem for deformations of complex structure on ALE Kahler surfaces, which will be used to prove that for any scalar-flat Kahler ALE surface, all small deformations of
-
Burkhard Wilking - Manifolds with almost nonnegative curvature operatorWilkingBurkhard
We show that n-manifolds with a lower volume bound v and upper diameter bound D whose curvature operator is bounded below by $-\varepsilon(n,v,D)$ also admit metrics with nonnegative curvature
-
Jean-Marc Schlenker - Anti-de Sitter geometry and polyhedra inscribed in quadricsSchlenkerJean-Marc
Anti-de Sitter geometry is a Lorentzian analog of hyperbolic geometry. In the last 25 years a number of connections have emerged between 3-dimensional anti-de Sitter geometry and the geometry of
-
Stéphane Saboureau - Sweep-outs, width estimates and volumeSabourauStéphane
Sweep-out techniques in geometry and topology have recently received a great deal of attention, leading to major breakthroughs. In this talk, we will present several width estimates relying on min-max
-
Igor Belegradek - Smoothness of Minkowski sum and generic rotationsBelegradekIgor
I will discuss whether the Minkowski sum of two compact convex bodies can be made smoother by a generic rotation of one of them. Here "generic" is understood in the sense of Baire category. The main
-
Feng Luo - Discrete conformal geometry of polyhedral surfaces and its convergenceLuoFeng
Our recent joint work with D. Gu established a discrete version of the uniformization theorem for compact polyhedral surfaces. In this talk, we prove that discrete uniformizaton maps converge to
-
Greg McShane - Volumes of hyperbolics manifolds and translation distances
Schlenker and Krasnov have established a remarkable Schlaffli-type formula for the (renormalized) volume of a quasi-Fuchsian manifold. Using this, some classical results in complex analysis and Gromov
-
David Gabai - Maximal cusps of low volumeGabaiDavid
With Robert Haraway, Robert Meyerhoff, Nathaniel Thurston and Andrew Yarmola. We address the following question. What are all the 1-cusped hyperbolic 3-manifolds whose maximal cusps have low volume?
-
Genevieve Walsh - Boundaries of Kleinian groupsWalshG.R.
We study the problem of classifying Kleinian groups via the topology of their limit sets. In particular, we are interested in one-ended convex-cocompact Kleinian groups where each piece in the JSJ