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On the cauchy problem for equivariant wave maps
Communications on Pure and Applied Mathematics, 1994The authors study wave maps from a Lorentzian manifold \(M^{n + 1}\) to a Riemann manifold \(N^ k\). The main assumption of the paper is that the manifold \(M^{n + 1}\) and the target manifold are both rotationally symmetric i.e. there exist an \(\text{SO}(n)\) action on \(M\) and an \(\text{SO}(k)\) action on \(N\).
Shatah, Jalal, Tahvildar-Zadeh, A. Shadi
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Free Groups and Almost Equivariant Maps
Bulletin of the London Mathematical Society, 1995Let \(G\) be a group. If \(\Omega\) and \(\Delta\) are (right) \(G\)-sets, a function \(\phi : \Omega \to \Delta\) is called an almost \(G\)-map if, for all \(g \in G\), the set \(\{\omega \in \Omega \mid (\phi \omega) g \neq \phi (\omega g)\}\) is finite. Let \(\{*\}\) denote the \(G\)-set consisting of a single \(G\)-fixed element, \(*\). If \(G\) is
Dicks, Warren, Kropholler, Peter H.
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On Equivariant Maps Between Spheres with Involutions
The Annals of Mathematics, 1969P: w~nn 1 -* Z (see [7, p. 271] and [8, Th. A]), thereby verifying a conjecture of Bredon. In view of [8, Th. A], it only remains to improve a divisibility relation by a factor of 2 in case n _ 0(4), n > 0. However this is a delicate matter and is accomplished by means of Adams operations in equivariant KO-theory.
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1996
Harmonic maps between Riemannian manifolds satisfy a system of quasi-linear partial differential equations. In order to have existence results one would solve PDE’s on certain manifolds. In the case when the sectional curvature of the target manifold is nonpositive or the image of the map is contained in a geodesic convex neighborhood, such a problem ...
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Harmonic maps between Riemannian manifolds satisfy a system of quasi-linear partial differential equations. In order to have existence results one would solve PDE’s on certain manifolds. In the case when the sectional curvature of the target manifold is nonpositive or the image of the map is contained in a geodesic convex neighborhood, such a problem ...
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Iaworowski's theorem on the extension of equivariant maps
Russian Mathematical Surveys, 1984The main result of the note is the following version of Jaworowski's equivariant extension theorem. Let G be a compact Lie group, let X be a separable metric G-space and A be a closed invariant subset of X such that \(X\setminus A\) is of finite number of orbit types and \(\dim (X\setminus A)\leq n+1.\) Let \(f: A\to Y\) be an equivariant continuous ...
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Degree for Gradient Equivariant Maps and Equivariant Conley Index
1997In order to establish some notation and terminology we recall that if f : ℝ n → ℝ n is continuous and Ω is an open bounded subset of ℝ n such that f is different from 0 on the boundary of Ω, then there is defined an integer Deg(f, Ω) — the Brouwer (or topological) degree of f with respect to Ω.
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Fixed orbit index for equivariant maps
Nonlinear Analysis: Theory, Methods & Applications, 2001openaire +2 more sources