scholarly journals Interpolation Inequalities, Nonlinear Flows, Boundary Terms, Optimality and Linearization

2016 ◽  
Vol 2 (1-2) ◽  
pp. 267-295 ◽  
Author(s):  
Jean Dolbeault ◽  
Maria J. Esteban ◽  
Michael Loss
Keyword(s):  
Interpolation Inequalities ◽  
Boundary Terms ◽  
Nonlinear Flows

scholarly journals Interpolation inequalities on the sphere: linear vs. nonlinear flows

2017 ◽  
Vol 26 (2) ◽  
pp. 351-379 ◽  
Author(s):  
Jean Dolbeault ◽  
Maria J. Esteban ◽  
Michael Loss
Keyword(s):  
Interpolation Inequalities ◽  
Nonlinear Flows

scholarly journals Actions, topological terms and boundaries in first-order gravity: A review

2016 ◽  
Vol 25 (04) ◽  
pp. 1630011 ◽  
Author(s):  
Alejandro Corichi ◽  
Irais Rubalcava-García ◽  
Tatjana Vukašinac
Keyword(s):  
Boundary Conditions ◽  
Symplectic Structure ◽  
Equations Of Motion ◽  
Hamiltonian Formalism ◽  
Action Principle ◽  
Internal Boundary ◽  
Four Dimensions ◽  
First Order ◽  
Conserved Charges ◽  
Boundary Terms

In this review, we consider first-order gravity in four dimensions. In particular, we focus our attention in formulations where the fundamental variables are a tetrad [Formula: see text] and a [Formula: see text] connection [Formula: see text]. We study the most general action principle compatible with diffeomorphism invariance. This implies, in particular, considering besides the standard Einstein–Hilbert–Palatini term, other terms that either do not change the equations of motion, or are topological in nature. Having a well defined action principle sometimes involves the need for additional boundary terms, whose detailed form may depend on the particular boundary conditions at hand. In this work, we consider spacetimes that include a boundary at infinity, satisfying asymptotically flat boundary conditions and/or an internal boundary satisfying isolated horizons boundary conditions. We focus on the covariant Hamiltonian formalism where the phase space [Formula: see text] is given by solutions to the equations of motion. For each of the possible terms contributing to the action, we consider the well-posedness of the action, its finiteness, the contribution to the symplectic structure, and the Hamiltonian and Noether charges. For the chosen boundary conditions, standard boundary terms warrant a well posed theory. Furthermore, the boundary and topological terms do not contribute to the symplectic structure, nor the Hamiltonian conserved charges. The Noether conserved charges, on the other hand, do depend on such additional terms. The aim of this manuscript is to present a comprehensive and self-contained treatment of the subject, so the style is somewhat pedagogical. Furthermore, along the way, we point out and clarify some issues that have not been clearly understood in the literature.

scholarly journals A concise scheme of vegetation boundary terms in subtropical high mountains

2014 ◽  
Vol 9 (20) ◽  
pp. 1560-1570
Author(s):  
Chiu Ching-An ◽  
Lee Mei-Fen ◽  
Tzeng Hsy-Yu ◽  
Liao Min-Chun
Keyword(s):  
Subtropical High ◽  
High Mountains ◽  
Boundary Terms ◽  
Vegetation Boundary
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