Page 353 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 353
GEOMETRIC ANALYSIS AND LOW-DIMENSIONAL TOPOLOGY (MS-59)
generalized Willmore functional. This achieved via a perturbation argument starting from round
centered spheres in Schwarzschild space. These foliations can be interpreted as a center of mass
as measured by the generalized Willmore functional.
Time permitting we will discuss the existence and regularity of critical points of generalized
Willmore functionals in a more general setting.
The results presented are based on the a corresponding analysis for the Willmore functional
by T. Lamm, J. Metzger and F. Schulze, and are part of the authors Ph.D. thesis.
A two-valued Bernstein theorem in dimension four
Fritz Hiesmayr, f.hiesmayr@ucl.ac.uk
University College London, United Kingdom
The Bernstein theorem is a classical result in geometric analysis, which states that entire mini-
mal graphs are linear in all dimensions up to eight. Here we present a generalisation to so-called
two-valued minimal graphs. These are graphs of two-valued functions, which are singular ge-
ometric objects that model the behaviour of minimal hypersurfaces near branch points. The
two-valued Bernstein theorem we present proves that entire two-valued minimal graphs are
linear in dimension four.
Characterizing slopes for Legendrian knots
Marc Kegel, kegemarc@math.hu-berlin.de
Humboldt-Universität zu Berlin, Germany
From a given Legendrian knot K in the standard contact 3-sphere, we can construct a symplectic
4-manifold WK by attaching a Weinstein 2-handle along K to the 4-ball. In this talk, we will
construct non-equivalent Legendrian knots K and K such that WK and WK are equivalent. On
the other hand, we will discuss an example of a Legendrian knot K that is characterized by its
symplectic 4-manifold WK. This is based on joint work with Roger Casals and John Etnyre.
No previous knowledge of contact geometry is assumed. We will discuss all relevant no-
tions.
Large area-constrained Willmore spheres in initial data sets
Thomas Koerber, thomas.koerber@univie.ac.at
University of Vienna, Austria
Coauthor: Michael Eichmair
Area-constrained Willmore spheres are surfaces that are particularly well-adapted to the Hawk-
ing mass, a local measure of the gravitational field of initial data sets for isolated gravitational
systems. In this talk, I will present recent results (joint with M. Eichmair) on the existence and
uniqueness of large area-constrained Willmore surfaces in such initial data sets. In particular,
I will describe necessary and sufficient conditions on the scalar curvature of the initial data set
that guarantee the existence of a unique asymptotic foliation by large area-constrained Willmore
spheres. I will also discuss recent results on the geometric center of mass of this foliation.
351
generalized Willmore functional. This achieved via a perturbation argument starting from round
centered spheres in Schwarzschild space. These foliations can be interpreted as a center of mass
as measured by the generalized Willmore functional.
Time permitting we will discuss the existence and regularity of critical points of generalized
Willmore functionals in a more general setting.
The results presented are based on the a corresponding analysis for the Willmore functional
by T. Lamm, J. Metzger and F. Schulze, and are part of the authors Ph.D. thesis.
A two-valued Bernstein theorem in dimension four
Fritz Hiesmayr, f.hiesmayr@ucl.ac.uk
University College London, United Kingdom
The Bernstein theorem is a classical result in geometric analysis, which states that entire mini-
mal graphs are linear in all dimensions up to eight. Here we present a generalisation to so-called
two-valued minimal graphs. These are graphs of two-valued functions, which are singular ge-
ometric objects that model the behaviour of minimal hypersurfaces near branch points. The
two-valued Bernstein theorem we present proves that entire two-valued minimal graphs are
linear in dimension four.
Characterizing slopes for Legendrian knots
Marc Kegel, kegemarc@math.hu-berlin.de
Humboldt-Universität zu Berlin, Germany
From a given Legendrian knot K in the standard contact 3-sphere, we can construct a symplectic
4-manifold WK by attaching a Weinstein 2-handle along K to the 4-ball. In this talk, we will
construct non-equivalent Legendrian knots K and K such that WK and WK are equivalent. On
the other hand, we will discuss an example of a Legendrian knot K that is characterized by its
symplectic 4-manifold WK. This is based on joint work with Roger Casals and John Etnyre.
No previous knowledge of contact geometry is assumed. We will discuss all relevant no-
tions.
Large area-constrained Willmore spheres in initial data sets
Thomas Koerber, thomas.koerber@univie.ac.at
University of Vienna, Austria
Coauthor: Michael Eichmair
Area-constrained Willmore spheres are surfaces that are particularly well-adapted to the Hawk-
ing mass, a local measure of the gravitational field of initial data sets for isolated gravitational
systems. In this talk, I will present recent results (joint with M. Eichmair) on the existence and
uniqueness of large area-constrained Willmore surfaces in such initial data sets. In particular,
I will describe necessary and sufficient conditions on the scalar curvature of the initial data set
that guarantee the existence of a unique asymptotic foliation by large area-constrained Willmore
spheres. I will also discuss recent results on the geometric center of mass of this foliation.
351
