scholarly journals Characterization of Large Isoperimetric Regions in Asymptotically Hyperbolic Initial Data

2019 ◽  
Vol 368 (2) ◽  
pp. 777-798
Author(s):  
Otis Chodosh ◽  
Michael Eichmair ◽  
Yuguang Shi ◽  
Jintian Zhu
Keyword(s):  
Initial Data ◽  
Isoperimetric Regions ◽  
Asymptotically Hyperbolic

scholarly journals The Jang Equation and the Positive Mass Theorem in the Asymptotically Hyperbolic Setting

2021 ◽  
Author(s):  
Anna Sakovich
Keyword(s):  
Initial Data ◽  
Spatial Dimension ◽  
Positive Mass Theorem ◽  
Positive Mass ◽  
Asymptotically Hyperbolic ◽  
Jang Equation

AbstractWe solve the Jang equation with respect to asymptotically hyperbolic “hyperboloidal” initial data. The results are applied to give a non-spinor proof of the positive mass theorem in the asymptotically hyperbolic setting. This work focuses on the case when the spatial dimension is equal to three.

scholarly journals On the Center of Mass of Asymptotically Hyperbolic Initial Data Sets

2015 ◽  
Vol 17 (6) ◽  
pp. 1505-1528 ◽  
Author(s):  
Carla Cederbaum ◽  
Julien Cortier ◽  
Anna Sakovich
Keyword(s):  
Initial Data ◽  
Center Of Mass ◽  
Data Sets ◽  
Asymptotically Hyperbolic

PATTERN FORMATION, WAVE PROPAGATION AND STABILITY IN CONSERVATION LAWS WITH SLOW DIFFUSION AND FAST REACTION

2004 ◽  
Vol 01 (04) ◽  
pp. 605-626 ◽  
Author(s):  
HAITAO FAN ◽  
HAILIANG LIU
Keyword(s):  
Initial Data ◽  
Fast Reaction ◽  
Limiting Behavior ◽  
Wave Speeds ◽  
Slow Diffusion ◽  
Scalar Conservation Law ◽  
Scalar Conservation ◽  
Short Time ◽  
Shock Layers

The limiting behavior of the solution of a scalar conservation law with slow diffusion and fast bistable reaction is considered. In a short time the solution develops transition patterns connected by shock layers and rarefaction layers, when the initial data has finitely many monotone pieces. The existence and uniqueness of the front profiles for both shock layers and rarefaction layers are established. A variational characterization of wave speeds of these profiles is derived. These profiles are shown to be stable. Furthermore, it is proved that solutions with monotone initial data approach the shock layer or rarefaction layer waves as time goes to infinity.

Characterization of Schwarzschildean initial data

2005 ◽  
Vol 72 (8) ◽  
Author(s):  
Juan Antonio Valiente Kroon
Keyword(s):  
Initial Data

Stability of a thermoelastic mixture with second sound

2018 ◽  
Vol 24 (6) ◽  
pp. 1692-1706 ◽  
Author(s):  
Margareth S. Alves ◽  
Marcio V. Ferreira ◽  
Jaime E. Muñoz Rivera ◽  
O. Vera Villagrán
Keyword(s):  
Initial Data ◽  
Asymptotic Properties ◽  
Sufficient Conditions ◽  
Complete Characterization ◽  
Second Sound ◽  
Dimensional Model ◽  
One Dimensional ◽  
The One ◽  
Necessary And Sufficient

We consider the one-dimensional model of a thermoelastic mixture with second sound. We give a complete characterization of the asymptotic properties of the model in terms of the coefficients of the model. We establish the necessary and sufficient conditions for the model to be exponential or polynomial stable and also the conditions for which there exist initial data for where the energy is conserved.

scholarly journals Spacetime Positive Mass Theorems for Initial Data Sets with Non-Compact Boundary

2020 ◽  
Author(s):  
Sérgio Almaraz ◽  
Levi Lopes de Lima ◽  
Luciano Mari
Keyword(s):  
Initial Data ◽  
Energy Conditions ◽  
Data Sets ◽  
Positive Mass ◽  
Momentum Vector ◽  
Asymptotically Flat ◽  
The Common ◽  
Underlying Manifold ◽  
Asymptotically Hyperbolic ◽  
Compact Boundary

Abstract In this paper, we define an energy-momentum vector at the spatial infinity of either asymptotically flat or asymptotically hyperbolic initial data sets carrying a non-compact boundary. Under suitable dominant energy conditions (DECs) imposed both on the interior and along the boundary, we prove the corresponding positive mass inequalities under the assumption that the underlying manifold is spin. In the asymptotically flat case, we also prove a rigidity statement when the energy-momentum vector is light-like. Our treatment aims to underline both the common features and the differences between the asymptotically Euclidean and hyperbolic settings, especially regarding the boundary DECs.

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