On Capacitary Characteristics of Noncompact Riemannian Manifolds

2021 ◽  
Vol 65 (3) ◽  
pp. 61-67
Author(s):  
A. G. Losev ◽  
V. V. Filatov
Keyword(s):  
Riemannian Manifolds ◽  
Noncompact Riemannian Manifolds

scholarly journals Nonexistence for hyperbolic problems on Riemannian manifolds1

2020 ◽  
Vol 120 (1-2) ◽  
pp. 87-101
Author(s):  
Dario D. Monticelli ◽  
Fabio Punzo ◽  
Marco Squassina
Keyword(s):  
Euclidean Space ◽  
Riemannian Manifolds ◽  
Wave Operator ◽  
Existence Of Solutions ◽  
Necessary Conditions ◽  
Hyperbolic Problems ◽  
Power Nonlinearity ◽  
General Weight ◽  
Noncompact Riemannian Manifolds ◽  
General Weight Function

We establish necessary conditions for the existence of solutions to a class of semilinear hyperbolic problems defined on complete noncompact Riemannian manifolds, extending some nonexistence results for the wave operator with power nonlinearity on the whole Euclidean space. A general weight function depending on spacetime is allowed in front of the power nonlinearity.

scholarly journals WHITE NOISE ANALYSIS ON MANIFOLDS AND THE ENERGY REPRESENTATION OF A GAUGE GROUP

2010 ◽  
Vol 13 (04) ◽  
pp. 619-627
Author(s):  
TAKAHIRO HASEBE
Keyword(s):  
Riemannian Manifold ◽  
White Noise ◽  
Gauge Group ◽  
Riemannian Manifolds ◽  
Differential Operators ◽  
Noise Analysis ◽  
White Noise Analysis ◽  
Analysis On Manifolds ◽  
Noncompact Riemannian Manifolds

The energy representation of a gauge group on a Riemannian manifold has been discussed by several authors. Y. Shimada has shown the irreducibility with the use of white noise analysis for compact Riemannian manifolds. In this paper we extend its technique to the noncompact Riemannian manifolds which have differential operators satisfying some conditions.

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