Conformally Invariant Extremal Problems and Quasiconformal Maps

1992 ◽  
Vol 43 (4) ◽  
pp. 501-514 ◽  
Author(s):  
M. Vuorinen
Keyword(s):  
Extremal Problems ◽  
Quasiconformal Maps ◽  
Conformally Invariant

scholarly journals Extremal length and Dirichlet problem on Klein surfaces

2019 ◽  
Vol 39 (2) ◽  
pp. 281-296
Author(s):  
Monica Roşiu
Keyword(s):  
Dirichlet Problem ◽  
Extremal Length ◽  
Extremal Problems ◽  
Klein Surface ◽  
Klein Surfaces ◽  
Conformally Invariant ◽  
Extremal Distance

The object of this paper is to extend the method of extremal length to Klein surfaces by solving conformally invariant extremal problems on the complex double. Within this method we define the extremal length, the extremal distance, the conjugate extremal distance, the modulus, the reduced extremal distance on a Klein surface and we study their dependences on arcs.

scholarly journals On conformally invariant extremal problems

2009 ◽  
Vol 3 (1) ◽  
pp. 97-119 ◽  
Author(s):  
Vesna Manojlovic
Keyword(s):  
Euclidean Space ◽  
Metric Spaces ◽  
Extremal Problems ◽  
Invariant Metrics ◽  
Conformal Invariants ◽  
Conformally Invariant

This paper deals with conformal invariants in the euclidean space Rn, n ? 2, and their interrelation. In particular, conformally invariant metrics and balls of the respective metric spaces are studied.

Teichmuller Geometry

2017 ◽  
Author(s):  
Benson Farb ◽  
Dan Margalit
Keyword(s):  
Uniqueness Theorem ◽  
Existence Theorems ◽  
Quadratic Differentials ◽  
Complex Structures ◽  
Metric Geometry ◽  
Quasiconformal Maps ◽  
Hyperbolic Structures ◽  
Teichmüller Metric ◽  
Uniqueness And Existence ◽  
Teichmüller Mapping

This chapter focuses on the metric geometry of Teichmüller space. It first explains how one can think of Teich(Sɡ) as the space of complex structures on Sɡ. To this end, the chapter defines quasiconformal maps between surfaces and presents a solution to the resulting Teichmüller's extremal problem. It also considers the correspondence between complex structures and hyperbolic structures, along with the Teichmüller mapping, Teichmüller metric, and the proof of Teichmüller's uniqueness and existence theorems. The fundamental connection between Teichmüller's theorems, holomorphic quadratic differentials, and measured foliations is discussed as well. Finally, the chapter describes the Grötzsch's problem, whose solution is tied to the proof of Teichmüller's uniqueness theorem.

Some Extremal Problems in (D, D+1)-Regular Graphs

2016 ◽  
Vol 6 (2) ◽  
pp. 105
Author(s):  
N. Murugesan ◽  
R. Anitha
Keyword(s):  
Extremal Problems ◽  
Regular Graphs

CASIMIR EFFECT FOR THE ROBIN SURFACES IN STATIC ROBERTSON–WALKER SPACE–TIME

2011 ◽  
Vol 20 (02) ◽  
pp. 161-168 ◽  
Author(s):  
MOHAMMAD R. SETARE ◽  
M. DEHGHANI
Keyword(s):  
Scalar Field ◽  
Energy Momentum Tensor ◽  
Casimir Effect ◽  
Vacuum Expectation ◽  
Robin Boundary Condition ◽  
Momentum Tensor ◽  
Space Time ◽  
Conformally Invariant ◽  
Time Space ◽  
Robin Boundary

We investigate the energy–momentum tensor for a massless conformally coupled scalar field in the region between two curved surfaces in k = -1 static Robertson–Walker space–time. We assume that the scalar field satisfies the Robin boundary condition on the surfaces. Robertson–Walker space–time space is conformally related to Rindler space; as a result we can obtain vacuum expectation values of the energy–momentum tensor for a conformally invariant field in Robertson–Walker space–time space from the corresponding Rindler counterpart by the conformal transformation.

Field equations in the neighbourhood of a particle in a conformal theory of gravitation. II

1969 ◽  
Vol 313 (1512) ◽  
pp. 71-82 ◽  
Keyword(s):  
Local Geometry ◽  
Field Equations ◽  
Schwarzschild Solution ◽  
Conformal Theory ◽  
Conformally Invariant ◽  
Coordinate Singularity ◽  
Previous Solution ◽  
Theory Of Gravitation ◽  
Spherically Symmetric Metric ◽  
Radial Variable

The field equations in the neighbourhood of a particle for a spherically symmetric metric in the conformal theory of gravitation put forward by Hoyle & Narlikar are examined. As the theory is conformally invariant, one can use different but physically equivalent conformal frames to study the equations. Previously these equations were studied in a conformal frame which, though suitable far away from the isolated particle, turns out not to be suitable in the neighbourhood of the particle. In the present paper a solution in a conformal frame is obtained that is suitable for considering regions near the particle. The solution thus obtained differs from the previous one in several respects. For example, it has no coordinate singularity for any non-zero value of the radial variable, unlike the previous solution or the Schwarzschild solution. It is also shown with the use of this solution that in this theory distant matter has an effect on local geometry.

Extremal Problems Involving the Two Largest Complementarity Eigenvalues of a Graph

2019 ◽  
Vol 36 (1) ◽  
pp. 1-25 ◽  
Author(s):  
Alberto Seeger ◽  
David Sossa
Keyword(s):  
Extremal Problems
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