Willmore surfaces
Dienstag, 19.4.16, 16:15-17:15, Raum 404, Eckerstr. 1
Min-Max theory and the Willmore conjecture, Fernando C. Marques, André Neves
Dienstag, 26.4.16, 16:15-17:15, Raum 404, Eckerstr. 1
Existence of minimizing Willmore Klein bottles in euclidean four-space
Dienstag, 3.5.16, 16:15-17:15, Raum 404, Eckerstr. 1
We consider immersed Klein bottles in euclidean four-space with low Willmore energy. It turns out that there are three distinct homotopy classes of immersions that are regularly homotopic to an embedding. One is characterized by the property that the immersions have Euler normal number zero. This class contains embedded Klein bottles with Willmore energy strictly less than \(8\bpi\). We prove that the infimum of the Willmore energy among all immersed Klein bottles in euclidean four-space is attained by a smooth embedding that is in this first homotopy class. In the other two homotopy classes we have that the Willmore energy is bounded from below by \(8\bpi\). We classify all immersed Klein bottles with Willmore energy \(8\bpi\) and Euler normal number \(+4\) or \(-4\). These surfaces are minimizers of the second or the third homotopy class.
Min-Max theory and the Willmore conjecture, Fernando C. Marques, André Neves
Dienstag, 10.5.16, 16:00-17:00, Raum 404, Eckerstr. 1
Min-Max theory and the Willmore conjecture, Fernando C. Marques, André Neves
Dienstag, 24.5.16, 16:15-17:15, Raum 404, Eckerstr. 1
The first Steklov eigenvalue
Dienstag, 31.5.16, 16:15-17:15, Raum 404, Eckerstr. 1
Sharp estimates for the principal eigenvalue of p-operators
Dienstag, 7.6.16, 16:15-17:15, Raum 404, Eckerstr. 1
Given a strongly elliptic operator L = div(A∇u) in divergence form, defined on a compact Riemannian manifold (possibly with strictly convex boundary), which satisfies BE(0, N ) we define a non-linear p−operator L p and use the intrinsic Γ 2 - calculus to prove the sharp estimate λ ≥ (p−1)π p p /D p for the principal eigenvalue of L p , where D denotes the diameter of M . Equality holds if and only if dim(M ) = 1 and L = ∆ g up to rescaling. We also derive the lower bound π 2 /D 2 +a/2 for the real part of the principal eigenvalue of non-symmetric operators L = div(A∇u) + B(u) satisfying BE(a, ∞).
Min-Max theory and the Willmore conjecture, Fernando C. Marques, André Neves
Dienstag, 21.6.16, 16:15-17:15, Raum 404, Eckerstr. 1
Min-Max theory and the Willmore conjecture, Fernando C. Marques, André Neves
Dienstag, 28.6.16, 16:15-17:15, Raum 404, Eckerstr. 1
A Möbius invariant decomposition of the Möbius energy
Dienstag, 5.7.16, 16:15-17:15, Raum 404, Eckerstr. 1
Abstract:\nWe consider the Möbius energy for closed curves in R^n\nso-called since it is invariant under Möbius transformations.\nWe can decompose the energy into three parts, each of which is\nMöoius invariant.\nThe decomposition gives is easy-to-analyze components, e.g., for\nderiving the first and second variational formulas and estimates, and\nfor giving information concerning the minimizers of the energiers.\nThis is a joint work with Dr. Aya Ishizeki (Saitama University)
Min-Max theory and the Willmore conjecture, Fernando C. Marques, André Neves
Dienstag, 12.7.16, 16:15-17:15, Raum 404, Eckerstr. 1
Variational formulae for the sigma_r energy
Dienstag, 19.7.16, 16:15-17:15, Raum 404, Eckerstr. 1