Singularities of the maximum function on a manifold with boundary

1986 ◽  
Vol 33 (4) ◽  
pp. 1103-1127 ◽  
Author(s):  
V. I. Matov
Keyword(s):  
Maximum Function ◽  
Manifold With Boundary

SINGULAR CYCLES AND Ck-ROBUST TRANSITIVE SET ON MANIFOLD WITH BOUNDARY

2011 ◽  
Vol 13 (02) ◽  
pp. 191-211 ◽  
Author(s):  
D. CARRASCO-OLIVERA ◽  
C. A. MORALES ◽  
B. SAN MARTÍN
Keyword(s):  
Vector Field ◽  
Vector Fields ◽  
Manifold With Boundary ◽  
Transitive Set ◽  
Singular Cycle ◽  
Hyperbolic Equilibrium

Let M be a 3-manifold with boundary ∂M. Let X be a C∞, vector field on M, tangent to ∂M, exhibiting a singular cycle associated to a hyperbolic equilibrium σ∈∂M with real eigenvalues λss < λs < 0 < λu satisfying λs - λss - 2λu > 0. We prove under generic conditions and k large enough the existence of a Ck robust transitive set of X, that is, any Ck vector field Ck close to X exhibits a transitive set containing the cycle. In particular, C∞ vector fields exhibiting Ck robust transitive sets, for k large enough, which are not singular-hyperbolic do exist on any compact 3-manifold with boundary.

scholarly journals Eleven-dimensional supergravity on a manifold with boundary

1996 ◽  
Vol 475 (1-2) ◽  
pp. 94-114 ◽  
Author(s):  
Petr Hořava ◽  
Edward Witten
Keyword(s):  
Manifold With Boundary

scholarly journals CONFIGURATION CATEGORIES AND HOMOTOPY AUTOMORPHISMS

2018 ◽  
Vol 62 (1) ◽  
pp. 13-41
Author(s):  
MICHAEL S. WEISS
Keyword(s):  
Compact Manifold ◽  
Geometric Conditions ◽  
Homeomorphism Group ◽  
Manifold With Boundary ◽  
Smooth Compact Manifold

AbstractLet M be a smooth compact manifold with boundary. Under some geometric conditions on M, a homotopical model for the pair (M, ∂M) can be recovered from the configuration category of M \ ∂M. The grouplike monoid of derived homotopy automorphisms of the configuration category of M \ ∂M then acts on the homotopical model of (M, ∂M). That action is compatible with a better known homotopical action of the homeomorphism group of M \ ∂M on (M, ∂M).

QUANTUM LIOUVILLE FIELD THEORY ON A MANIFOLD WITH BOUNDARY

1998 ◽  
Vol 13 (25) ◽  
pp. 2057-2063
Author(s):  
S. A. APIKYAN
Keyword(s):  
Field Theory ◽  
Functional Equations ◽  
Ward Identity ◽  
Semiclassical Approximation ◽  
Boundary Structure ◽  
Manifold With Boundary ◽  
Structure Constants ◽  
Liouville Field Theory

This letter studies the quantum Liouville field theory on a manifold with boundary. The boundary conformal Ward identity (CWI) is written and its semiclassical approximation is analyzed. This establishes a method of finding the accessory parameters of the theory with boundary. The boundary structure constants of the theory are defined and the functional equations which determine them are derived.

scholarly journals Embedding Topological $n$-Manifolds into Compact Nonstandard Topological $n$-Manifolds with Boundary

2021 ◽  
Author(s):  
Yu-Lin Chou
Keyword(s):  
Topological Manifold ◽  
Manifolds With Boundary ◽  
Manifold With Boundary ◽  
Topological Manifolds ◽  
One Point Compactification ◽  
Main Message

We show as a main message that there is a simple dimension-preserving way to openly and densely embed every topological manifold into a compact ``nonstandard'' topological manifold with boundary.This class of ``nonstandard'' topological manifolds with boundary contains the usual topological manifolds with boundary.In particular,the Alexandroff one-point compactification of every given topological $n$-manifold is a ``nonstandard'' topological $n$-manifold with boundary.

A generalization of the asymptotic behavior of Palais-Smale sequences on a manifold with boundary

2018 ◽  
Vol 29 (10) ◽  
pp. 1850069
Author(s):  
Hong Zhang
Keyword(s):  
Asymptotic Behavior ◽  
Boundary Value Problem ◽  
Mean Curvature ◽  
Compact Manifold ◽  
Boundary Value ◽  
Fundamental Solutions ◽  
Curvature Equation ◽  
Mean Curvature Equation ◽  
Manifold With Boundary ◽  
Prescribed Mean Curvature Equation

In this paper, we study the asymptotic behavior of Palais-Smale sequences associated with the prescribed mean curvature equation on a compact manifold with boundary. We prove that every such sequence converges to a solution of the associated equation plus finitely many “bubbles” obtained by rescaling fundamental solutions of the corresponding Euclidean boundary value problem.

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