On the operator of symmetric differentiation on a compact Riemannian manifold with boundary

1980 ◽  
Vol 74 (2) ◽  
pp. 143-164 ◽  
Author(s):  
V. Georgescu
Keyword(s):  
Riemannian Manifold ◽  
Compact Riemannian Manifold ◽  
Manifold With Boundary

scholarly journals Boundary layers to a singularly perturbed Klein–Gordon–Maxwell–Proca system on a compact Riemannian manifold with boundary

2017 ◽  
Vol 8 (1) ◽  
pp. 559-582 ◽  
Author(s):  
Mónica Clapp ◽  
Marco Ghimenti ◽  
Anna Maria Micheletti
Keyword(s):  
Riemannian Manifold ◽  
Boundary Conditions ◽  
Compact Riemannian Manifold ◽  
Semiclassical Limit ◽  
Arbitrary Dimension ◽  
Neumann Boundary ◽  
Perturbation Parameter ◽  
Singularly Perturbed ◽  
Manifold With Boundary ◽  
Klein Gordon

Abstract We study the semiclassical limit to a singularly perturbed nonlinear Klein–Gordon–Maxwell–Proca system, with Neumann boundary conditions, on a Riemannian manifold {\mathfrak{M}} with boundary. We exhibit examples of manifolds, of arbitrary dimension, on which these systems have a solution which concentrates at a closed submanifold of the boundary of {\mathfrak{M}} , forming a positive layer, as the singular perturbation parameter goes to zero. Our results allow supercritical nonlinearities and apply, in particular, to bounded domains in {\mathbb{R}^{N}} . Similar results are obtained for the more classical electrostatic Klein–Gordon–Maxwell system with appropriate boundary conditions.

EXTREMAL FUNCTIONS FOR MOSER–TRUDINGER INEQUALITIES ON 2-DIMENSIONAL COMPACT RIEMANNIAN MANIFOLDS WITH BOUNDARY

2006 ◽  
Vol 17 (03) ◽  
pp. 313-330 ◽  
Author(s):  
YUNYAN YANG
Keyword(s):  
Riemannian Manifold ◽  
Riemannian Manifolds ◽  
Compact Riemannian Manifold ◽  
Extremal Functions ◽  
Manifolds With Boundary ◽  
Manifold With Boundary ◽  
Blowing Up

Let (M,g) be a 2-dimensional compact Riemannian manifold with boundary. In this paper, we use the method of blowing up analysis to prove the existence of the extremal functions for some Moser–Trudinger inequalities on (M,g).

scholarly journals Hearing the shape of a compact Riemannian manifold with a finite number of piecewise impedance boundary conditions

1997 ◽  
Vol 20 (2) ◽  
pp. 397-402 ◽  
Author(s):  
E. M. E. Zayed
Keyword(s):  
Riemannian Manifold ◽  
Boundary Conditions ◽  
Finite Number ◽  
Spectral Function ◽  
Compact Riemannian Manifold ◽  
Smooth Boundary ◽  
Beltrami Operator ◽  
Smooth Functions ◽  
Impedance Boundary ◽  
Impedance Boundary Conditions

The spectral functionΘ(t)=∑i=1∞exp(−tλj), where{λj}j=1∞are the eigenvalues of the negative Laplace-Beltrami operator−Δ, is studied for a compact Riemannian manifoldΩof dimension “k” with a smooth boundary∂Ω, where a finite number of piecewise impedance boundary conditions(∂∂ni+γi)u=0on the parts∂Ωi(i=1,…,m)of the boundary∂Ωcan be considered, such that∂Ω=∪i=1m∂Ωi, andγi(i=1,…,m)are assumed to be smooth functions which are not strictly positive.

On the non-regularity of tangent sphere bundles

1978 ◽  
Vol 82 (1-2) ◽  
pp. 13-17 ◽  
Author(s):  
David E. Blair
Keyword(s):  
Riemannian Manifold ◽  
Large Class ◽  
Constant Curvature ◽  
Positive Constant ◽  
Contact Structure ◽  
Compact Riemannian Manifold ◽  
Contact Structures ◽  
Sphere Bundle ◽  
Contact Manifolds ◽  
Tangent Sphere

SynopsisClassically the tangent sphere bundles have formed a large class of contact manifolds; their contact structures are not in general regular, however. Specifically we prove that the natural contact structure on the tangent sphere bundle of a compact Riemannian manifold of non-positive constant curvature is not regular.

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