scholarly journals Definition of center of mass for isolated physical systems and unique foliations by stable spheres with constant mean curvature

1996 ◽  
Vol 124 (1-3) ◽  
pp. 281-311 ◽  
Author(s):  
Gerhard Huisken ◽  
Shing-Tung Yau
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Center Of Mass ◽  
Physical Systems ◽  
Definition Of

scholarly journals On center of mass and foliations by constant spacetime mean curvature surfaces for isolated systems in General Relativity

2021 ◽  
Vol 60 (6) ◽  
Author(s):  
Carla Cederbaum ◽  
Anna Sakovich
Keyword(s):  
Initial Data ◽  
Mean Curvature ◽  
Evolution Equations ◽  
Center Of Mass ◽  
Point Particle ◽  
Data Sets ◽  
Data Set ◽  
Definition Of ◽  
Isolated Systems ◽  
Invent Math

AbstractWe propose a new foliation of asymptotically Euclidean initial data sets by 2-spheres of constant spacetime mean curvature (STCMC). The leaves of the foliation have the STCMC-property regardless of the initial data set in which the foliation is constructed which asserts that there is a plethora of STCMC 2-spheres in a neighborhood of spatial infinity of any asymptotically flat spacetime. The STCMC-foliation can be understood as a equivariant relativistic generalization of the CMC-foliation suggested by Huisken and Yau (Invent Math 124:281–311, 1996). We show that a unique STCMC-foliation exists near infinity of any asymptotically Euclidean initial data set with non-vanishing energy which allows for the definition of a new notion of total center of mass for isolated systems. This STCMC-center of mass transforms equivariantly under the asymptotic Poincaré group of the ambient spacetime and in particular evolves under the Einstein evolution equations like a point particle in Special Relativity. The new definition also remedies subtle deficiencies in the CMC-approach to defining the total center of mass suggested by Huisken and Yau (Invent Math 124:281–311, 1996) which were described by Cederbaum and Nerz (Ann Henri Poincaré 16:1609–1631, 2015).

scholarly journals On far-outlying constant mean curvature spheres in asymptotically flat Riemannian 3-manifolds

2020 ◽  
Vol 2020 (767) ◽  
pp. 161-191
Author(s):  
Otis Chodosh ◽  
Michael Eichmair
Keyword(s):  
Scalar Curvature ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Existence Results ◽  
Asymptotically Flat ◽  
Weingarten Surfaces ◽  
Differential Geom

AbstractWe extend the Lyapunov–Schmidt analysis of outlying stable constant mean curvature spheres in the work of S. Brendle and the second-named author [S. Brendle and M. Eichmair, Isoperimetric and Weingarten surfaces in the Schwarzschild manifold, J. Differential Geom. 94 2013, 3, 387–407] to the “far-off-center” regime and to include general Schwarzschild asymptotics. We obtain sharp existence and non-existence results for large stable constant mean curvature spheres that depend delicately on the behavior of scalar curvature at infinity.

Cloaked Droplets on Lubricant-Infused Surfaces: Union of Constant Mean Curvature Interfaces Dictated by Thin-Film Tension

Langmuir ◽  
2021 ◽  
Author(s):  
Madhu Ranjan Gunjan ◽  
Alok Kumar ◽  
Rishi Raj
Keyword(s):  
Thin Film ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Film Tension

scholarly journals Constant mean curvature surfaces with boundary on a sphere

2013 ◽  
Vol 220 ◽  
pp. 316-323 ◽  
Author(s):  
Rafael López ◽  
Juncheol Pyo
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Constant Mean Curvature Surfaces

Complete spacelike hypersurfaces in a Robertson–Walker spacetime

2011 ◽  
Vol 151 (2) ◽  
pp. 271-282 ◽  
Author(s):  
ALMA L. ALBUJER ◽  
FERNANDA E. C. CAMARGO ◽  
HENRIQUE F. DE LIMA
Keyword(s):  
Maximum Principle ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Rigidity Results ◽  
Complete Spacelike Hypersurfaces ◽  
Uniqueness Results ◽  
Spacelike Hypersurfaces ◽  
Generalized Maximum Principle ◽  
Non Parametric

AbstractIn this paper, as a suitable application of the well-known generalized maximum principle of Omori–Yau, we obtain uniqueness results concerning to complete spacelike hypersurfaces with constant mean curvature immersed in a Robertson–Walker (RW) spacetime. As an application of such uniqueness results for the case of vertical graphs in a RW spacetime, we also get non-parametric rigidity results.

scholarly journals LOWER BOUNDS FOR MORSE INDEX OF CONSTANT MEAN CURVATURE TORI

2002 ◽  
Vol 34 (05) ◽  
pp. 599-609 ◽  
Author(s):  
WAYNE ROSSMAN
Keyword(s):  
Lower Bounds ◽  
Mean Curvature ◽  
Morse Index ◽  
Constant Mean Curvature
Sign in / Sign up

Export Citation Format

Share Document