scholarly journals On the Yamabe problem and the scalar curvature problems under boundary conditions

2002 ◽  
Vol 322 (4) ◽  
pp. 667-699 ◽  
Author(s):  
Antonio Ambrosetti ◽  
YanYan Li ◽  
Andrea Malchiodi
Keyword(s):  
Boundary Conditions ◽  
Scalar Curvature ◽  
Yamabe Problem

On the conformal scalar curvature equations on Finsler manifolds

2016 ◽  
Vol 14 (01) ◽  
pp. 1750008
Author(s):  
Neda Shojaee ◽  
Morteza MirMohammad Rezaii
Keyword(s):  
Scalar Curvature ◽  
Finsler Geometry ◽  
Yamabe Problem ◽  
Finsler Manifolds ◽  
Yamabe Flow ◽  
Conformal Deformations

In this paper, we study conformal deformations and [Formula: see text]-conformal deformations of Ricci-directional and second type scalar curvatures on Finsler manifolds. Then we introduce the best equation to study the Yamabe problem on Finsler manifolds. Finally, we restrict conformal deformations of metrics to [Formula: see text]-conformal deformations and derive the Yamabe functional and the Yamabe flow in Finsler geometry.

Chern-Yamabe problem and Chern-Yamabe soliton

2021 ◽  
Vol 32 (03) ◽  
pp. 2150016
Author(s):  
Pak Tung Ho ◽  
Jinwoo Shin
Keyword(s):  
Scalar Curvature ◽  
Complex Manifold ◽  
The Other ◽  
Compact Complex Manifold ◽  
Yamabe Problem ◽  
Conformal Metric ◽  
Hermitian Metric ◽  
Dimension Formula ◽  
Complex Dimension ◽  
Yamabe Soliton

Let [Formula: see text] be a compact complex manifold of complex dimension [Formula: see text] endowed with a Hermitian metric [Formula: see text]. The Chern-Yamabe problem is to find a conformal metric of [Formula: see text] such that its Chern scalar curvature is constant. In this paper, we prove that the solution to the Chern-Yamabe problem is unique under some conditions. On the other hand, we obtain some results related to the Chern-Yamabe soliton.

scholarly journals Equivariant Yamabe problem with boundary

2022 ◽  
Vol 61 (1) ◽  
Author(s):  
Pak Tung Ho ◽  
Jinwoo Shin
Keyword(s):  
Scalar Curvature ◽  
Isometry Group ◽  
Yamabe Problem ◽  
Conformal Class ◽  
Invariant Metric

AbstractAs a generalization of the Yamabe problem, Hebey and Vaugon considered the equivariant Yamabe problem: for a subgroup G of the isometry group, find a G-invariant metric whose scalar curvature is constant in a given conformal class. In this paper, we study the equivariant Yamabe problem with boundary.

scholarly journals Prescribing the Scalar Curvature under Minimal Boundary Conditions on the Half Sphere

2002 ◽  
Vol 2 (2) ◽  
Author(s):  
Mohamed Ben Ayed ◽  
Khalil El Mehdi ◽  
Mohameden Ould Ahmedou
Keyword(s):  
Boundary Conditions ◽  
Variational Problem ◽  
Scalar Curvature ◽  
Critical Points ◽  
Existence Results ◽  
Topological Methods ◽  
Critical Points At Infinity

AbstractThis paper is devoted to the problem of prescribing the scalar curvature under zero boundary conditions. Using dynamical and topological methods involving the study of critical points at infinity of the associated variational problem, we prove some existence results on the standard half sphere.

Scalar curvature under boundary conditions

2000 ◽  
Vol 330 (11) ◽  
pp. 1013-1018 ◽  
Author(s):  
Antonio Ambrosetti ◽  
YanYan Li ◽  
Andrea Malchiodi
Keyword(s):  
Boundary Conditions ◽  
Scalar Curvature

Topological Tools in Prescribing the Scalar Curvature on the Half Sphere

2004 ◽  
Vol 4 (2) ◽  
Author(s):  
Mohamed Ben Ayed ◽  
Hichem Chtioui
Keyword(s):  
Boundary Conditions ◽  
Scalar Curvature ◽  
Existence Results ◽  
Topological Invariant

AbstractUsing a topological invariant, due to Bahri [4], and dynamical methods, we prove some existence results for the problem prescribing the scalar curvature under zero boundary conditions on the standard half sphere.

scholarly journals Compactness and non-compactness for the Yamabe problem on manifolds with boundary

2017 ◽  
Vol 2017 (724) ◽  
Author(s):  
Marcelo M. Disconzi ◽  
Marcus A. Khuri
Keyword(s):  
Scalar Curvature ◽  
Mean Curvature ◽  
Constant Scalar Curvature ◽  
Yamabe Problem ◽  
Riemannian Structure ◽  
Manifolds With Boundary ◽  
Conformal Deformation ◽  
Zero Mean Curvature

AbstractWe study the problem of conformal deformation of Riemannian structure to constant scalar curvature with zero mean curvature on the boundary. We prove compactness for the full set of solutions when the boundary is umbilic and the dimension

Use of the Magnetostatic Analogue In Electromagnetic Lens Engineering

1970 ◽  
Vol 28 ◽  
pp. 360-361
Author(s):  
John W. Coleman
Keyword(s):  
Boundary Conditions ◽  
High Performance ◽  
Force Fields ◽  
Optical Design ◽  
Direct Conversion ◽  
Design Engineering ◽  
Design Data ◽  
Scalar Potentials ◽  
Geometric Elements ◽  
At Will

In the design engineering of high performance electromagnetic lenses, the direct conversion of electron optical design data into drawings for reliable hardware is oftentimes difficult, especially in terms of how to mount parts to each other, how to tolerance dimensions, and how to specify finishes. An answer to this is in the use of magnetostatic analytics, corresponding to boundary conditions for the optical design. With such models, the magnetostatic force on a test pole along the axis may be examined, and in this way one may obtain priority listings for holding dimensions, relieving stresses, etc..The development of magnetostatic models most easily proceeds from the derivation of scalar potentials of separate geometric elements. These potentials can then be conbined at will because of the superposition characteristic of conservative force fields.

A digital vocal tract simulator with boundary conditions at lips and glottis

1981 ◽  
Vol 64 (11) ◽  
pp. 18-26 ◽  
Author(s):  
Tetsuya Nomura ◽  
Nobuhiro Miki ◽  
Nobuo Nagai
Keyword(s):  
Boundary Conditions ◽  
Vocal Tract
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