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The author considers the Klein-Gordon equation for $(1 + 1)$ -dimensional flat spacetime. He is interested in those coordinate systems for which the equation is separable. These coordinate systems are explicitly known and generally do not cover the whole plane. The author constructs tensor fields which he can use to express the locus of points where the coordinates break down.

Local approximation of uniformly regular Carnot–Carathéodory quasispaces by their tangent cones.

Greshnov, A.V. (2007)

Sibirskij Matematicheskij Zhurnal

Local Boundary Regularity of the Canonical Einstein-Kähler Metric on Pseudoconvex Domains.

John S. Bland (1983)

Mathematische Annalen

Local constraints on Einstein-Weyl geometries.

M.G. Eastwood, K.P. Tod (1997)

Journal für die reine und angewandte Mathematik

Local convexifiability of some rigid domains

Kolář, Martin (2005)

Proceedings of the 24th Winter School "Geometry and Physics"

Local convexity and nonnegative curvature - Gromov's proof of the sphere theorem.

J.-H. Eschenburg (1986)

Inventiones mathematicae

Local coordinates for $SL (n, C)$ -character varieties of finite-volume hyperbolic 3-manifolds

Pere Menal-Ferrer, Joan Porti (2012)

Annales mathématiques Blaise Pascal

Given a finite-volume hyperbolic 3-manifold, we compose a lift of the holonomy in $SL (2, C)$ with the $n$ -dimensional irreducible representation of $SL (2, C)$ in $SL (n, C)$ . In this paper we give local coordinates of the $SL (n, C)$ -character variety around the character of this representation. As a corollary, this representation is isolated among all representations that are unipotent at the cusps.

Local existence of Ricci Solitons.

Thomas A. Ivey (1996)

Manuscripta mathematica

Local gradient estimates of $p$ -harmonic functions, $1 / H$ -flow, and an entropy formula

Brett Kotschwar, Lei Ni (2009)

Annales scientifiques de l'École Normale Supérieure

In the first part of this paper, we prove local interior and boundary gradient estimates for $p$ -harmonic functions on general Riemannian manifolds. With these estimates, following the strategy in recent work of R. Moser, we prove an existence theorem for weak solutions to the level set formulation of the $1 / H$ (inverse mean curvature) flow for hypersurfaces in ambient manifolds satisfying a sharp volume growth assumption. In the second part of this paper, we consider two parabolic analogues of the $p$ -harmonic...

Local invariants of a pseudo-Riemannian manifold.

Peter B. Gilkey (1975)

Mathematica Scandinavica

Local isometric immersions of R2 into R4.

M. Dajczer, M. Do Carmo (1993)

Journal für die reine und angewandte Mathematik

Local isometry classes of Riemannian $3$ -manifolds with constant Ricci eigenvalues $ρ_{1} = ρ_{2} \neq ρ_{3} > 0$

Oldřich Kowalski, Masami Sekizawa (1996)

Archivum Mathematicum

Local monotonicity of Hausdorff measures restricted to curves in $ℝ^{n}$

Robert Černý (2009)

Commentationes Mathematicae Universitatis Carolinae

We give a sufficient condition for a curve $γ : ℝ \to ℝ^{n}$ to ensure that the $1$ -dimensional Hausdorff measure restricted to $γ$ is locally monotone.

Local monotonicity of Hausdorff measures restricted to real analytic curves

Robert Černý (2010)

Commentationes Mathematicae Universitatis Carolinae

We prove that the 1-dimensional Hausdorff measure restricted to a simple real analytic curve $γ : ℝ \to ℝ^{N}$ , $N \geq 2$ , is locally 1-monotone.

Local monotonicity of measures supported by graphs of convex functions.

Robert Cerný (2004)

Publicacions Matemàtiques

Local reduction theorems and invariants for singular contact structures

Bronislaw Jakubczyk, Michail Zhitomirskii (2001)

Annales de l’institut Fourier

A differential 1-form on a $(2 k + 1)$ -dimensional manifolds $M$ defines a singular contact structure if the set $S$ of points where the contact condition is not satisfied, $S = {p \in M : (ω \land {(d ω)}^{k} (p) = 0}$ , is nowhere dense in $M$ . Then $S$ is a hypersurface with singularities and the restriction of $ω$ to $S$ can be defined. Our first theorem states that in the holomorphic, real-analytic, and smooth categories the germ of Pfaffian equation $(ω)$ generated by $ω$ is determined, up to a diffeomorphism, by its restriction to $S$ , if we eliminate certain degenerated singularities...

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