scholarly journals Rigidity of Compact Fuchsian Manifolds with Convex Boundary

2021 ◽  
Author(s):  
Roman Prosanov
Keyword(s):  
Boundary Component ◽  
Convex Boundary ◽  
Manifold With Boundary ◽  
Induced Path

Abstract A compact Fuchsian manifold with boundary is a hyperbolic 3-manifold homeomorphic to $S_g \times [0; 1]$ such that the boundary component $S_g \times \{ 0\}$ is geodesic. We prove that a compact Fuchsian manifold with convex boundary is uniquely determined by the induced path metric on $S_g \times \{1\}$. We do not put further restrictions on the boundary except convexity.

scholarly journals Comparison theorems for manifolds with mean convex boundary

2015 ◽  
Vol 17 (05) ◽  
pp. 1550010 ◽  
Author(s):  
Jian Ge
Keyword(s):  
Upper Bound ◽  
Mean Curvature ◽  
Space Form ◽  
Sharp Estimate ◽  
Comparison Theorems ◽  
First Eigenvalue ◽  
Convex Boundary ◽  
Manifold With Boundary ◽  
The Mean ◽  
Mean Convex

Let Mn be an n-dimensional Riemannian manifold with boundary ∂M. Assuming that Ricci curvature is bounded from below by (n - 1)k, for k ∈ ℝ, we give a sharp estimate of the upper bound of ρ(x) = d (x, ∂M), in terms of the mean curvature bound of the boundary. When ∂M is compact, the upper bound is achieved if and only if M is isometric to a disk in space form. A Kähler version of estimation is also proved. Moreover, we prove a Laplacian comparison theorem for distance function to the boundary of Kähler manifold and also estimate the first eigenvalue of the real Laplacian.

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.

The influence of interacting strain rates on turbulence in convex boundary layers

1996 ◽  
Vol 8 (11) ◽  
pp. 3163-3171 ◽  
Author(s):  
Andreas C. Schwarz ◽  
Michael W. Plesniak
Keyword(s):  
Boundary Layers ◽  
Strain Rates ◽  
Convex 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.

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