18,722 research outputs found
Existence of translating solutions to the flow by powers of mean curvature on unbounded domains
In this paper, we prove the existence of classical solutions of the Dirichlet
problem for a class of quasi-linear elliptic equations on unbounded domains
like a cone or a U-type domain. This problem comes from the study of mean
curvature flow and its generalization, the flow by powers of mean curvature.
Our approach is a modified version of the classical Perron method, where the
solutions to the minimal surface equation are used as sub-solutions and a
family auxiliary functions are constructed as super-solutions.Comment: 30 page
Rigorous constraints on the matrix elements of the energy-momentum tensor
The structure of the matrix elements of the energy-momentum tensor play an
important role in determining the properties of the form factors ,
and which appear in the Lorentz covariant decomposition
of the matrix elements. In this paper we apply a rigorous frame-independent
distributional-matching approach to the matrix elements of the Poincar\'{e}
generators in order to derive constraints on these form factors as . In contrast to the literature, we explicitly demonstrate that
the vanishing of the anomalous gravitomagnetic moment and the condition
are independent of one another, and that these constraints are not
related to the specific properties or conservation of the individual
Poincar\'{e} generators themselves, but are in fact a consequence of the
physical on-shell requirement of the states in the matrix elements and the
manner in which these states transform under Poincar\'{e} transformations.Comment: 11 pages; v2: additional comments added, matches published versio
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