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. Small eigenvalues of surfaces - old and new,
    (with W. Ballmann and S. Mondal).
    arxiv

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

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

  5. On the bottom of spectra under coverings,
    Mathematische Zeitschrift, online first.
    (with W. Ballmann and P. Polymerakis)
    arxiv journal

  6. On the analytic systole of Riemannian surfaces of finite type,
    Geometric and Functional Analysis, 27 (2017), 1070-1105.
    (with W. Ballmann and S. Mondal)
    arxiv journal

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

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

  9. Small eigenvalues of closed surfaces,
    Journal of Differential Geometry 103 (2016), 1-13.
    (with W. Ballmann and S. Mondal)
    arxiv journal
Talks
19.10.2017 Existence of metrics maximizing the first eigenvalue on closed surfaces, Oberseminar Differentialgeometrie, MPIM Bonn
12.10.2017 Existence of metrics maximizing the first eigenvalue on closed surfaces, Geometric Analysis at Roscoff, Roscoff
14.09.2017 Existence of metrics maximizing the first eigenvalue on closed surfaces, Metric Measure Spaces and Ricci Curvature, MPIM Bonn
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 Graduate Seminar on Differential Geometry: Yamabe problem (with Werner Ballmann, Bogdan Georgiev, Anna Siffert)
SS 16 Exercise class for Geometry 1 by Manuel Amann
WS 15/16 Graduate Seminar on Differential Geometry: Steklov eigenvalues and minimal surfaces (with Werner Ballmann, Bogdan Georgiev, Anna Siffert)
WS 15/16 Exercise class for Global Analysis 1 by Ursula Hamenstädt
SS 15 Graduate Seminar on Differential Geometry: Willmore conjecture (with Werner Ballmann, Bogdan Georgiev, Fabian Spiegel)
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

Geometric Analysis Learning Seminar
schedule