News

I will teach a mini-course on The Penrose inequality in extrinsic geometry at the summer school Geometry and Gravity.

Bio

I am PI of the Principal Investigator Project 10.55776/PAT9828924 of the Austrian Science Fund (FWF) at the University of Vienna. Previously, I was PI of the Lise Meitner Programme 10.55776/M3184 with Michael Eichmair as co-PI.
I obtained my doctoral degree at the University of Freiburg in 2020 under the supervision of Guofang Wang.
During my doctorate, I spent time at University College London as a visiting research student of Felix Schulze.
I won the Ferdinand-von-Lindemann-Preis for the best doctoral thesis and the Alumni Prize for the best master thesis of the Mathematical Institute of the University of Freiburg.

Contact

Faculty of Mathematics
Oskar-Morgenstern-Platz 1
1090 Vienna

Email: thomas.koerber@univie.ac.at

ORCID: 0000-0003-1676-0824

Pronouns: he/him

Research

Preprints

• The Penrose inequality in extrinsic geometry (with Michael Eichmair)
  submitted. [arXiv:2411.02113]
• On the Minkowski inequality near the sphere (with Otis Chodosh and Michael Eichmair)
  submitted. [arXiv:2306.03848]
• Schoen's conjecture for limits of isoperimetric surfaces (with Michael Eichmair)
  submitted. [arXiv:2303.12200]

Publications

• Foliations of asymptotically flat 3-manifolds by stable constant mean curvature spheres (with Michael Eichmair)
  Journal of Differential Geometry, 128 (2024), no. 3, 1037-1083. [journal] [arXiv:2201.12081]
• Inverse mean curvature flow and Ricci-pinched three-manifolds (with Gerhard Huisken)
  Journal für die reine und angewandte Mathematik 814 (2024), 1-8. [journal] [arXiv:2305.04702]
• Huisken-Yau-type uniqueness for area-constrained Willmore spheres (with Michael Eichmair, Jan Metzger, and Felix Schulze)
  Duke Mathematical Journal, 173 (2024), no. 9, 1677-1730. [journal] [arXiv:2204.04102]
• Large area-constrained Willmore surfaces in asymptotically Schwarzschild 3-manifolds (with Michael Eichmair)
  Journal of Differential Geometry, 127 (2024), no. 1, 105-160. [journal] [arXiv:2101.12665]
• The Riemannian Penrose inequality for asymptotically flat manifolds with non-compact boundary
  Journal of Differential Geometry, 124 (2023), no. 2, 317-379. [journal] [arXiv:1909.13283]
• Doubling of asymptotically flat half-spaces and the Riemannian Penrose inequality (with Michael Eichmair)
  Communications in Mathematical Physics, 400 (2023), no. 3, 1823–1860. [journal] [arXiv:2302.00175]
• The Willmore center of mass of initial data sets (with Michael Eichmair)
  Communications in Mathematical Physics, 392 (2022), no. 2, 483-516. [journal] [arXiv:2201.12077]
• A free boundary isometric embedding problem in the unit ball
  Calculus of Variations and Partial Differential Equations, 61 (2022), no. 2, Paper No. 50, 36 pp. [journal] [arXiv:1908.11188]
• The area preserving Willmore flow and local maximizers of the Hawking mass in asymptotically Schwarzschild manifolds
  The Journal of Geometric Analysis, 31 (2021), no. 4, 3455–3497. [journal] [arXiv:1810.12866]
• Sharp estimates for the principal eigenvalue of the p-operator
  Calculus of Variations and Partial Differential Equations, 57 (2018), no. 2, Paper No. 49, 30 pp. [journal] [arXiv:1907.10957]

Upcoming talks

• January 2025, Geometry Seminar, University of Trento
• May 2025, Oberseminar Geometrische Analysis und Mathematische Relativitätstheorie, University of Tübingen
• July 2025, Österreichisches und süddeutsches Kolloquium, Vienna University of Technology

Talks

• The Penrose inequality in extrinsic geometry
  December 2024, Geometry Seminar, Karlsruhe Institute of Technology
• The Penrose inequality in extrinsic geometry
  November 2024, Gromov, Hanke, Sormani, Yu's Not Only Scalar Curvature Seminar
• The Penrose inequality in extrinsic geometry
  October 2024, Nonlinear Partial Differential Equations in Salzburg, University of Salzburg
• The Penrose inequality in extrinsic geometry
  October 2024, Nonlinear Partial Differential Equations in Freiburg, University of Freiburg
• Inverse mean curvature flow and Ricci-pinched three-manifolds
  April 2024, Leipzig General Relativity Seminar, University of Leipzig
• Schoen's conjecture for limits of isoperimetric surfaces
  February 2024, Analysis, Geometry and Topology of Positive Scalar Curvature Metrics, Oberwolfach Research Institute for Mathematics
• Schoen's conjecture for limits of isoperimetric surfaces
  December 2023, Mathematical Relativity: Past, Present, Future, Erwin Schrödinger International Institute for Mathematics and Physics
• Schoen's conjecture for limits of isoperimetric surfaces
  November 2023, Partial Differential Equations Seminar, University of Oxford
• Schoen's conjecture for limits of isoperimetric surfaces
  November 2023, Analysis Seminar, University of Warwick
• Inverse mean curvature flow and Ricci-pinched three-manifolds
  October 2023, Geometry and Topology Seminar, University of Vienna
• Inverse mean curvature flow and Ricci-pinched three-manifolds
  September 2023, Guess what? A Pisan workshop in Geometric Analysis, Centro De Giorgi
• Schoen's conjecture for limits of isoperimetric surfaces
  April 2023, Vienna Geometric Analysis Seminar, University of Vienna
• Schoen's conjecture for limits of isoperimetric surfaces
  March 2023, Gordon Workshop Geometric Analysis with focus on Geometric Flows, Hebrew University
• Schoen's conjecture for limits of isoperimetric surfaces
  February 2023, Geometry and Topology Seminar, Duke University
• Schoen's conjecture for limits of isoperimetric surfaces
  January 2023, Geometry and Analysis Seminar, Columbia University
• The Riemannian Penrose inequality for asymptotically flat half-spaces and rigidity
  December 2022, Geometric Analysis Seminar, University of Miami
• The Riemannian Penrose inequality for asymptotically flat half-spaces and rigidity
  October 2022, Seminar der Gravitationsphysik, University of Vienna
• Uniqueness of large area-constrained Willmore spheres in initial data sets
  July 2022, Joint Online Mathematical Relativity Colloquium (JoMaReC)
• Foliations of asymptotically flat 3-manifolds by stable constant mean curvature spheres
  May 2022, CMC Seminar, University of Potsdam and University of Tübingen
• Foliations of asymptotically flat 3-manifolds by stable constant mean curvature spheres
  March 2022, Geometric Analysis and Partial Differential Equations Mini-Symposium, SIAM Conference on Analysis of Partial Differential Equations
• The Willmore center of mass
  March 2022, Gravitational Physics Lunch Seminar, University of Vienna
• Large area-constrained Willmore spheres in asymptotically Schwarzschild 3-manifolds
  November 2021, Geometric Analysis, Differential Geometry and Relativity, University of Potsdam and University of Tübingen
• Foliations of asymptotically flat 3-manifolds by stable constant mean curvature spheres
  November 2021, B.O.W.L. on-line seminar
• Foliations of asymptotically flat 3-manifolds by stable constant mean curvature spheres
  September 2021, Section Calculus of Variations and Geometric Analysis, DMV-ÖMG Annual Conference 2021
• Large area-constrained Willmore spheres in asymptotically Schwarzschild 3-manifolds
  September 2021, Research Seminar: Geometric Analysis, University of Copenhagen
• Large area-constrained Willmore spheres in initial data sets
  June 2021, Geometric Analysis and Low-Dimensional Topology Mini-Symposium, 8th European Congress of Mathematics
• Large area-constrained Willmore surfaces in asymptotically Schwarzschild 3-manifolds
  April 2021, Oberseminar Geometrische Analysis und Mathematische Relativitätstheorie, University of Tübingen
• Large area-constrained Willmore surfaces in asymptotically Schwarzschild 3-manifolds
  February 2021, Geometry Seminar, Stanford University
• Large area-constrained Willmore surfaces in asymptotically Schwarzschild 3-manifolds
  February 2021, Geometry and Analysis Seminar, Columbia University
• The Riemannian Penrose inequality for asymptotically flat manifolds with a non-compact boundary
  January 2020, Geometry Seminar, University of Turin
• The Riemannian Penrose inequality for asymptotically flat manifolds with a non-compact boundary
  January 2020, Geometry Seminar, Paris Diderot University
• The Riemannian Penrose inequality for asymptotically flat manifolds with a non-compact boundary
  November 2019, Geometry Seminar, University of Vienna
• Maximizers of the Hawking mass in asymptotically flat manifolds
  November 2018, Topics in Geometric Analysis Seminar, Free University of Berlin

Service

• Together with Anastasia Molchanova and Fabian Rupp, I am organizing the Vienna Geometric Analysis Seminar.
• I taught a mini-course on Geometric foliations in general relativity.
• Together with Michael Eichmair, I organized the Young PDEs Mini Symposium.

I have acted as referee for the following journals.

• Annals of Mathematics
• Advances in Mathematics
• Duke Mathematical Journal
• Communications on Pure and Applied Mathematics
• Calculus of Variations and Partial Differential Equations
• International Mathematics Research Notices
• Journal für die reine und angewandte Mathematik
• Journal of Differential Geometry
• Letters in Mathematical Physics
• Nonlinear Analysis
• The Journal of Geometric Analysis
• The Royal Society of Edinburgh: Proceedings A

Teaching and supervision

Past teaching

• Geometric analysis
  Winter 2023, lecturer
• Analysis on manifolds
  Summer 2023, teaching assistant
• Stochastics for secondary school teacher accreditation programme
  Winter 2022, teaching assistant
• Linear algebra and geometry 1
  Summer 2021, teaching assistant
• Calculus of variations
  Summer 2019, teaching assistant
• Calculus of variations
  Winter 2018, teaching assistant
• Introduction to convex analysis
  Summer 2018, teaching assistant
• Analysis 3,
  Winter 2017, teaching assistant
• Calculus of variations in dimension one
  Winter 2017, teaching assistant
• Differential geometry
  Summer 2017, teaching assistant

Past supervision

• Ein Beweis der Faber-Krahn-Ungleichung
  Summer 2023, bachelor thesis