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Institut für Mathematik
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Oberseminar Geometrische Analysis​​

Termin und Ort:

Dienstag 14 Uhr c.t., RM10 - 903; ab SoSe 2026 Raum 902

Veranstalter:

Prof. Dr. A. Bernig
Prof. Dr. J. Scheuer
Prof. Dr. T. Weth

Geometrische Analysis

Jun 16 2026
14:00

R

 Ben Lambert (Leeds)

Geometrische Analysis

Jun 9 2026
14:00

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

Qiyu Zhou (Australian National University)

Geometrische Analysis

Mai 5 2026
14:00

Raum 902

Mario Ishikawa (Wien)

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

Geometrische Analysis

Feb 3 2026
14:00

Raum 903

Mohammad Ivaki (Wien): Capillary Curvature Problems 

I will survey recent progress on the capillary Christoffel–Minkowski problem and its L_p analogue in the half-space. I will then discuss some of the main open problems in the area.

Geometrische Analysis

Jan 27 2026
14:00

Raum 903

Luca Iffland (Frankfurt): The local logarithmic Brunn-Minkowski inequality for bodies of revolution 

The conjectured logarithmic Brunn-Minkowski inequality is a stronger version of the classical Brunn-Minkowski inequality, that has many applications in convex geometry, stochastis and other fields of mathematics. In my recent work, I prove a local version of the logarithmic Brunn-Minkowski inequality for one body of revolution and
one arbitrary body. Equality cases are discussed and some consequences such as the logarithmic Minkowski inequality and the uniqueness of the cone volume measure for bodies of revolution are deduced. The proof uses an operator theoretic approach together with the decomposition of spherical functions into isotypical components with respect to rotations around a fixed axis