TY  - JOUR
A1  - Lamm, Tobias
A1  - Metzger, Jan
T1  - Minimizers of the willmore functional with a small area constraint
JF  - ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE
N2  - 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 small enough. Moreover, we partially classify complete surfaces of Willmore type with positive mean curvature in Riemannian three-manifolds.
KW  - Willmore functional
KW  - Minimizers
KW  - Direct method
Y1  - 2013
U6  - https://doi.org/10.1016/j.anihpc.2012.10.003
SN  - 0294-1449
VL  - 30
IS  - 3
SP  - 497
EP  - 518
PB  - Elsevier
CY  - Paris
ER  - 
TY  - JOUR
A1  - Lamm, Tobias
A1  - Metzger, Jan
A1  - Schulze, Felix
T1  - Foliations of asymptotically flat manifolds by surfaces of Willmore type
JF  - Mathematische Annalen
N2  - The goal of this paper is to establish the existence of a foliation of the asymptotic region of an asymptotically flat manifold with positive mass by surfaces which are critical points of the Willmore functional subject to an area constraint. Equivalently these surfaces are critical points of the Geroch-Hawking mass. Thus our result has applications in the theory of general relativity.
Y1  - 2011
U6  - https://doi.org/10.1007/s00208-010-0550-2
SN  - 0025-5831
VL  - 350
IS  - 1
SP  - 1
EP  - 78
PB  - Springer
CY  - New York
ER  -