scholarly journals On open scattering channels for a branched covering of the Euclidean plane

2021 ◽  
Author(s):  
Rainer Hempel ◽  
Olaf Post
Keyword(s):  
Euclidean Plane ◽  
Branched Covering

scholarly journals Cutoff AdS3 versus $$ T\overline{T} $$ CFT2 in the large central charge sector: correlators of energy-momentum tensor

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Yi Li ◽  
Yang Zhou
Keyword(s):  
Field Theory ◽  
Euclidean Plane ◽  
Energy Momentum Tensor ◽  
Central Charge ◽  
Momentum Tensor ◽  
Two Dimensional ◽  
Conformal Field ◽  
Operator Identity ◽  
Pure Gravity ◽  
Charge Sector

Abstract In this article we probe the proposed holographic duality between $$ T\overline{T} $$ T T ¯ deformed two dimensional conformal field theory and the gravity theory of AdS3 with a Dirichlet cutoff by computing correlators of energy-momentum tensor. We focus on the large central charge sector of the $$ T\overline{T} $$ T T ¯ CFT in a Euclidean plane and a sphere, and compute the correlators of energy-momentum tensor using an operator identity promoted from the classical trace relation. The result agrees with a computation of classical pure gravity in Euclidean AdS3 with the corresponding cutoff surface, given a holographic dictionary which identifies gravity parameters with $$ T\overline{T} $$ T T ¯ CFT parameters.

scholarly journals Harmonic branched coverings and uniformization of CAT(k) spheres

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Christine Breiner ◽  
Chikako Mese
Keyword(s):  
Harmonic Map ◽  
Branched Coverings ◽  
Curvature Bound ◽  
Branched Covering

Abstract Let S be a surface with a metric d satisfying an upper curvature bound in the sense of Alexandrov (i.e. via triangle comparison). We show that an almost conformal harmonic map from a surface into ( S , d ) {(S,d)} is a branched covering. As a consequence, if ( S , d ) {(S,d)} is homeomorphically equivalent to the 2-sphere 𝕊 2 {\mathbb{S}^{2}} , then it is conformally equivalent to 𝕊 2 {\mathbb{S}^{2}} .

scholarly journals On Negligible and Absolutely Nonmeasurable Subsets of the Euclidean Plane

2004 ◽  
Vol 11 (3) ◽  
pp. 479-487
Author(s):  
A. Kharazishvili
Keyword(s):  
Euclidean Plane ◽  
Identity Transformation ◽  
Extension Problem ◽  
Measure Extension ◽  
Nonmeasurable Set

Abstract The notions of a negligible set and of an absolutely nonmeasurable set are introduced and discussed in connection with the measure extension problem. In particular, it is demonstrated that there exist subsets of the plane 𝐑2 which are 𝑇2-negligible and, simultaneously, 𝐺-absolutely nonmeasurable. Here 𝑇2 denotes the group of all translations of 𝐑2 and 𝐺 denotes the group generated by {𝑔} ∪ 𝑇2, where 𝑔 is an arbitrary rotation of 𝐑2 distinct from the identity transformation and all central symmetries of 𝐑2.

An evaluation of the Jones polynomial of a parallel link

1988 ◽  
Vol 104 (1) ◽  
pp. 105-113
Author(s):  
Makoto Sakuma
Keyword(s):  
Jones Polynomial ◽  
Branched Covering ◽  
Parallel Link ◽  
Image Position

The Jones polynomial VL(t) of a link L in S3 contains certain information on the homology of the 2-fold branched covering D(L) of S3 branched along L. The following formulae are proved by Jones[3] and Lickorish and Millett[6] respectively:

Grade of Service Steiner Minimum Trees in the Euclidean Plane

Algorithmica ◽  
2001 ◽  
Vol 31 (4) ◽  
pp. 479-500 ◽  
Author(s):  
Xue ◽  
-H. Lin ◽  
-Z. Du
Keyword(s):  
Euclidean Plane ◽  
Grade Of Service

Construction and visualization of branched covering spaces

2016 ◽  
Author(s):  
Sanaz Golbabaei ◽  
Lawrence Roy ◽  
Prashant Kumar ◽  
Eugene Zhang
Keyword(s):  
Covering Spaces ◽  
Branched Covering

scholarly journals How to Collect Balls Moving in the Euclidean Plane

2004 ◽  
Vol 91 ◽  
pp. 229-245 ◽  
Author(s):  
Yuichi Asahiro ◽  
Takashi Horiyama ◽  
Kazuhisa Makino ◽  
Hirotaka Ono ◽  
Toshinori Sakuma ◽  
...  
Keyword(s):  
Euclidean Plane

Generalized evolutes of planar curves

2021 ◽  
Author(s):  
Yongqiao Wang ◽  
Yuan Chang ◽  
Haiming Liu
Keyword(s):  
Euclidean Plane ◽  
Singular Points ◽  
Moving Frames ◽  
Planar Curves ◽  
Fixed Direction ◽  
Spatial Curves

The evolutes of regular curves in the Euclidean plane are given by the caustics of regular curves. In this paper, we define the generalized evolutes of planar curves which are spatial curves, and the projection of generalized evolutes along a fixed direction are the evolutes. We also prove that the generalized evolutes are the locus of centers of slant circles of the curvature of planar curves. Moreover, we define the generalized parallels of planar curves and show that the singular points of generalized parallels sweep out the generalized evolute. In general, we cannot define the generalized evolutes at the singular points of planar curves, but we can define the generalized evolutes of fronts by using moving frames along fronts and curvatures of the Legendre immersion. Then we study the behaviors of generalized evolutes at the singular points of fronts. Finally, we give some examples to show the generalized evolutes.

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