scholarly journals Trudinger-Moser inequalities on a closed Riemannian surface with the action of a finite isometric group

2020 ◽  
Vol 20 (4) ◽  
pp. 1295-1324
Author(s):  
Yu Fang ◽  
Yunyan Yang
Keyword(s):  
Riemannian Surface

Expansive geodesic flows on surfaces

1993 ◽  
Vol 13 (1) ◽  
pp. 153-165 ◽  
Author(s):  
Miguel Paternain
Keyword(s):  
Geodesic Flow ◽  
Compact Surface ◽  
Conjugate Points ◽  
Riemannian Surface ◽  
Geodesic Flows ◽  
Flows On Surfaces

AbstractWe prove the following result: if M is a compact Riemannian surface whose geodesic flow is expansive, then M has no conjugate points. This result and the techniques of E. Ghys imply that all expansive geodesic flows of a compact surface are topologically equivalent.

Problems of Harmonic Analysis Related to Finite-Type Hypersurfaces in R3, and Newton Polyhedra Detlef Müller

2014 ◽  
Keyword(s):  
Harmonic Analysis ◽  
Finite Type ◽  
Maximal Function ◽  
Oscillatory Integrals ◽  
The Other ◽  
Riemannian Surface ◽  
Fourier Restriction ◽  
Newton Polyhedra ◽  
The Given ◽  
Finite Type Hypersurfaces

This chapter presents three sets of problems and explains how these questions can be answered in an (almost) complete way in terms of Newton polyhedra associated to the given surface S (here, a smooth, finite type hypersurface in R³ with Riemannian surface measure dσ‎). The first problem is a classical question about estimates for oscillatory integrals, and there exists a huge body of results on it, in particular for convex hypersurfaces. The other two problems had first been formulated by Stein: the study of maximal averages along hypersurfaces has been initiated in Stein's work on the spherical maximal function, and also the idea of Fourier restriction goes back to him.

Surface Mesh Generation in Parametric Space Using a Riemannian Surface Definition

2020 ◽  
Vol 13 (2) ◽  
pp. 476-484
Author(s):  
Cui Dai ◽  
Zhaoxue Wang ◽  
Liang Dong ◽  
Yiping Chen ◽  
Junfeng Qiu
Keyword(s):  
Mesh Generation ◽  
Riemannian Surface ◽  
Surface Mesh ◽  
Parametric Space ◽  
Surface Mesh Generation

scholarly journals An existence result for the mean-field equation on compact surfaces in a doubly supercritical regime

2013 ◽  
Vol 143 (5) ◽  
pp. 1021-1045 ◽  
Author(s):  
Aleks Jevnikar
Keyword(s):  
Field Equation ◽  
Existence Result ◽  
Mean Field ◽  
Type Inequality ◽  
Riemannian Surface ◽  
Supercritical Regime ◽  
Supercritical Parameters ◽  
The Mean ◽  
First Time ◽  
Mean Field Equation

We consider a class of variational equations with exponential nonlinearities on a compact Riemannian surface, describing the mean-field equation of the equilibrium turbulence with arbitrarily signed vortices. For the first time, we consider the problem with both supercritical parameters and we give an existence result by using variational methods. In doing so, we present a new Moser–Trudinger-type inequality under suitable conditions on the centre of mass and the scale of concentration of both eu and e−u, where u is the unknown function in the equation.

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