76 citations · 279 across the 20 of their papers we have counts for
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Local space time constant mean curvature and constant expansion foliations
Jan Metzger, Alejandro Peñuela Diaz
Inspired by the small sphere-limit for quasi-local energy we study local foliations of surfaces with prescribed mean curvature. Following the strategy used by Ye in 1991 to study l…
Huisken-Yau-type uniqueness for area-constrained Willmore spheres
Michael Eichmair, Thomas Koerber, Jan Metzger +1
Let be a Riemannian -manifold that is asymptotic to Schwarzschild. We study the existence of large area-constrained Willmore spheres with non-negative Hawki…
Refined position estimates for surfaces of Willmore type in Riemannian manifolds
Jan Metzger
In this paper we consider surfaces which are critical points of the Willmore functional subject to constrained area. In the case of small area we calculate the corrections to the i…
Local foliation of manifolds by surfaces of Willmore type
Tobias Lamm, Jan Metzger, Felix Schulze
We show the existence of a local foliation of a three dimensional Riemannian manifold by critical points of the Willmore functional subject to a small area constraint around non-de…
Willmore flow of surfaces in Riemannian spaces I: Concentration-compactness
Jan Metzger, Glen Wheeler, Valentina-Mira Wheeler
In this paper we study the local regularity of closed surfaces immersed in a Riemannian 3-manifold flowing by Willmore flow. We establish a pair of concentration-compactness altern…
Jenkins-Serrin type results for the Jang equation
Michael Eichmair, Jan Metzger
Let (M, g, k) be an initial data set for the Einstein equations of general relativity. We prove that there exist solutions of the Plateau problem for marginally outer trapped surfa…
Unique isoperimetric foliations of asymptotically flat manifolds in all dimensions
Michael Eichmair, Jan Metzger
We describe explicitly the large volume isoperimetric regions of a natural class of asymptotically flat manifolds, in any dimension. These isoperimetric regions detect the mass and…
Minimizers of the Willmore functional with a small area constraint
Tobias Lamm, Jan Metzger
We show the existence of a smooth spherical surface minimizing the Willmore functional subject to an area constraint in a compact Riemannian three-manifold, provided the area is sm…
On large volume preserving stable constant mean curvature surfaces in asymptotically flat manifolds
Michael Eichmair, Jan Metzger
Let (M,g) be a complete 3-dimensional asymptotically flat manifold with everywhere positive scalar curvature. We prove that, given a compact subset K of M, all volume preserving st…
Large isoperimetric surfaces in initial data sets
Michael Eichmair, Jan Metzger
We study the isoperimetric structure of asymptotically flat Riemannian 3-manifolds (M,g) that are C^0-asymptotic to Schwarzschild of mass m>0. Refining an argument due to H. Bray w…
Small surfaces of Willmore type in Riemannian manifolds
T. Lamm, J. Metzger
In this paper we investigate the properties of small surfaces of Willmore type in Riemannian manifolds. By \emph{small} surfaces we mean topological spheres contained in a geodesic…
Foliations of asymptotically flat manifolds by surfaces of Willmore type
Tobias Lamm, Jan Metzger, Felix Schulze
The goal of this paper is to establish the existence of a foliation of the asymptotic region of an asymptotically flat manifold with nonzero mass by surfaces which are critical poi…
Surfaces with maximal constant mean curvature
Jan Metzger
In this note we consider asymptotically flat manifolds with non-negative scalar curvature and an inner boundary which is an outermost minimal surface. We show that there exists an…
Foliations of asymptotically flat 3-manifolds by 2-surfaces of prescribed mean curvature
Jan Metzger
We construct 2-surfaces of prescribed mean curvature in 3-manifolds carrying asymptotically flat initial data for an isolated gravitating sysqtem with rather general decay conditio…