Henrik Matthiesen










Hi, I am a third year graduate student at MPIM Bonn funded by the IMPRS. My advisor is Werner Ballmann.
From February through Juli 2017 I was at MIT as a visiting graduate student supervised by Tobias Colding.
I am interested in geometric analysis. So far, I have mainly worked on questions related to the spectrum of the Laplace operator on functions.
At the moment I try to delve more into minimal surfaces and mean curvature flow.

Contact
Office: 215
Max Planck Institute for Mathematics
Vivatsgasse 7
53111 Bonn
Germany
mail: hematt(at)mpim-bonn.mpg.de

Research
Here is a list of my papers:

  1. Regularity of extremal metrics for Laplace eigenvalues in a conformal class,
    in preparation.

  2. Existence of metrics maximizing the first eigenvalue on closed surfaces,
    submitted.
    (with A. Siffert)
    arxiv

  3. Extremal metrics for Laplace eigenvalues in perturbed conformal classes on products,
    submitted.
    arxiv

  4. On the bottom of spectra under coverings,
    Mathematische Zeitschrift, to appear.
    (with W. Ballmann and P. Polymerakis)
    arxiv

  5. On the analytic systole of Riemannian surfaces of finite type,
    Geometric and Functional Analysis, to appear.
    (with W. Ballmann and S. Mondal)
    arxiv

  6. Regularity of conformal metrics with large first eigenvalue,
    Annales de la faculté des sciences de Toulouse Sér. 6 25 (2016), 1079-1094.
    arxiv journal

  7. Small eigenvalues of surfaces of finite type,
    Compositio Mathematica 153 (2017), 1747-1768.
    (with W. Ballmann and S. Mondal)
    arxiv journal

  8. Small eigenvalues of closed surfaces,
    Journal of Differential Geometry 103 (2016), 1-13.
    (with W. Ballmann and S. Mondal)
    arxiv journal
Talks
09.-13.10.2017 Existence of metrics maximizing the first eigenvalue on closed surfaces, Geometric Analysis at Roscoff, Roscoff (upcoming)
14.09.2017 Existence of metrics maximizing the first eigenvalue on closed surfaces, Metric Measure Spaces and Ricci Curvature, MPIM Bonn (upcoming)
29.06.2017 Existence of metrics maximizing the first eigenvalue on closed surfaces, Geometric Analysis Seminar, University of Chicago
21.06.2017 Existence of metrics maximizing the first eigenvalue on closed surfaces, Workshop on geometric spectral theory, Université de Neuchâtel
02.12.2016 Extremal metrics for Laplace eigenvalues in perturbed conformal classes, Séminaire de géométrie, Université de Nantes
17.06.2016 The analytic systole of Riemannian surfaces, Oberseminar Geometrie, Topologie und Analysis, Universität zu Köln
28.07.2015 Small eigenvalues of the Laplacian on surfaces, Workshop on Curvature and Global Shape, Universität Münster

Teaching
I am currently not teaching.
Previous teaching:

SS 16 Exercise class for Geometry 1 by Manuel Amann
WS 15/16 Exercise class for Global Analysis 1 by Ursula Hamenstädt
SS 15 Exercise class for Advanced Geometry 1 by Gabriela Weitze-Schmithüsen
WS 14/15 Exercise class for Algebraic Topology 2 by Ursula Hamenstädt
SS 14 Exercise class for Algebraic Topology 1 by Ursula Hamenstädt
WS 13/14 Exercise class for Topology 1 by Ursula Hamenstädt
SS 13 Exercise class for Introduction to Geometry and Topology by Thomas Vogel
WS 12/13 Exercise class for Analysis 1 by Benjamin Schlein