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Institut für Mathematik
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Oberseminar Geometrische Analysis​​

 

Jul 14 2026
14:00

Oscar Ortega Moreno (Madrid)

Geometrische Analysis

Jun 23 2026
14:00

Raum 902

Franz Schuster (Wien)

Geometrische Analysis

Jun 16 2026
14:00

Raum 902

 Ben Lambert (Leeds)

Geometrische Analysis

Jun 9 2026
14:00

Raum 902 - Vortrag zur Masterarbeit

Efe Akbayir (Frankfurt)

Geometrische Analysis

Mai 19 2026
14:00

Raum 902

Enea Parini (Aix-Marseille Université)

Geometrische Analysis

Mai 12 2026
14:00

Raum 902

Qiyu Zhou (Australian National University): High codimension mean curvature flow of spacelike-convex submanifolds with one spacelike codimension

In the pseudo-Euclidean space $\mathbb{R}^{n+1,k}$, we consider the mean curvature flow of $n$-dimensional spacelike submanifolds with spacelike codimension one and arbitrary timelike codimension $k$. We show that if the initial submanifold is compact and spacelike-convex (the acceleration along every geodesic is strictly spacelike), then natural quantities measuring curvature pinching and noncollapsing are preserved under the flow. Moreover, we prove an analogue of the Huisken and Gage-Hamilton theorems in this setting, which states that the mean curvature flow deforms any such submanifold to a point in finite time, and that the solution is asymptotic to a shrinking sphere in a maximally spacelike affine subspace $\mathbb{R}^{n+1,0}\subset \mathbb{R}^{n+1,k}$. 
 

Geometrische Analysis

Apr 28 2026
14:00

Raum 902

Tobias König (Frankfurt): Stability of reverse Sobolev-type inequalities on the sphere 

This talk is concerned with some recent results about the quantitative stability of Sobolev-type inequalities on the d-dimensional sphere. More precisely, I will present two different generalizations of the classical stability result by Bianchi and Egnell.

The first of these is the quantitative stability of the reverse fractional Sobolev inequality. Implementing the classical proof strategy by Bianchi and Egnell is non-trivial here because the underlying operator $A_{2s}$ is not positive definite when $s > d/2$. Remarkably, the case $s - d/2 \in (1,2)$ constitutes the first example of a Sobolev-type stability inequality (i) whose best constant is explicit and (ii) which does not admit an optimizer.

The second one concerns a fully nonlinear functional inequality for the $\sigma_2$-curvature. We prove its stability in a reverse setting occurring in three dimensions. As a geometric application, this implies a quantitative refinement of the almost-Schur lemma of De Lellis and Topping in the special case of the round 3-sphere. This is joint work with Jonas Peteranderl (LMU München).

Geometrische Analysis

Apr 14 2026
14:00

Raum 902

Ilka  Agricola (Marburg): Spectral theory on naturally reductive homogeneous spaces - theory and experiments 

The explicit computation of the spectrum of the Laplacian on closed Riemannian manifolds is a challenging task that only succeeds under strong symmetry assumptions. After the classical examples of spheres, projective spaces, and flat tori, Riemannian symmetric spaces G/K were the first large class of manifolds for which the spectrum could be computed explicitly via representation theoretic tools. The crucial point is that the connection induced from the canonical principal fibre bundle projection G →G/K is just the Levi-Civita connection, and the Laplacian can be identified with the Casimir operator.
For homogeneous spaces, this approach fails. I will explain how connections with torsion are used to „classify“ homogeneous spaces and how the task can be achieved for large families of naturally reductive homogeneous metrics. Many examples like Aloff-Wallach manifolds will be used to illustrate the results; in fact, explicit spectra were computed using Python and are available as a Jupyter notebook.

Geometrische Analysis

Mär 17 2026
14:00

Raum 903

Giorgio Saracco (Ferrara, Italien): The prescribed mean curvature equation under low regularity assumptions

Given an open set Omega and a positive constant H, does it exist a cartesian hypersurface defined on Omega whose mean curvature is constantly H? Equivalently, can one find a function u on Omega, whose graph has mean curvature constantly H? This question leads to the nonlinear elliptic prescribed mean curvature PDE.

Foundational results by Concus, Finn, and Giusti establish that, assuming Omega is Lipschitz, there exists a geometric threshold h(Omega) such that existence of solutions is guaranteed if H>h(Omega), while non existence occurs for H<h(Omega). Interesting phenomena arise at the threshold. As proved by Giusti, in the physically relevant case, that is, Omega is 2-dimensional, and assuming C^2 convexity, an elegant geometric criterion in terms on the curvature of Omega characterizes the regimes of existence and non-existence.

In a series of works partly in collaboration with Gian Paolo Leonardi, we extend these results to low regularity settings by removing the Lipschitz assumption on Omega. This necessitates developing a refined functional framework, including the introduction of Gauss—Green formulas under weak regularity conditions. Moreover, we generalize the two-dimensional geometric criterion by relaxing convexity assumptions and relying solely on appropriate one-sided bounds on the reach of Omega.

Geometrische Analysis

Feb 10 2026
14:00

Raum 903

Miles Simon (Magdeburg) - fällt aus