A Geometric Study of Wasserstein Spaces: Isometric Rigidity in Negative Curvature

In this paper, we initiate a geometric study of graph braid groups. More precisely, by applying the formalism of special colorings introduced in a previous paper, we determine precisely when a graph braid group is Gromov-hyperbolic, toral relatively hyperbolic and acylindrically hyperbolic.

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Flots magnétiques en courbure négative

Ergodic Theory and Dynamical Systems ◽

10.1017/s0143385799126634 ◽

1999 ◽

Vol 19 (2) ◽

pp. 413-436 ◽

Cited By ~ 6

Author(s):

STÉPHANE GROGNET

Keyword(s):

Magnetic Field ◽

Riemannian Manifold ◽

Geodesic Flow ◽

Negative Curvature ◽

Closed Surface ◽

Magnetic Flow ◽

Closed Riemannian Manifold ◽

Dynamical Properties ◽

Geometric Study

Consider a magnetic field on a closed Riemannian manifold of negative curvature. A geometric study provides dynamical properties of the associated flow stronger than expected for general perturbations of the geodesic flow. Under natural assumptions, a magnetic flow on a closed surface cannot be ${\mathcal C}^1$-conjugate to a geodesic flow.

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Highly Sensitive Temperature Sensor Based on Surface Plasmon Resonance in a Liquid-filled Hollow-core Negative-curvature Fiber

Optik ◽

10.1016/j.ijleo.2021.166970 ◽

2021 ◽

pp. 166970

Author(s):

Ying Han ◽

Lin Gong ◽

Fanchao Meng ◽

Hailiang Chen ◽

Yan Wang ◽

...

Keyword(s):

Surface Plasmon Resonance ◽

Surface Plasmon ◽

Plasmon Resonance ◽

Temperature Sensor ◽

Negative Curvature ◽

Hollow Core ◽

Highly Sensitive

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Hyperbolic Center of Mass for a System of Particles in a Two-Dimensional Space with Constant Negative Curvature: An Application to the Curved 2-Body Problem

Mathematics ◽

10.3390/math9050531 ◽

2021 ◽

Vol 9 (5) ◽

pp. 531

Author(s):

Pedro Pablo Ortega Palencia ◽

Ruben Dario Ortiz Ortiz ◽

Ana Magnolia Marin Ramirez

Keyword(s):

Negative Curvature ◽

Dimensional Space ◽

Center Of Mass ◽

Simple Expression ◽

Two Dimensional ◽

Constant Negative Curvature ◽

Euclidean Case ◽

System Of Particles ◽

Material Points ◽

The One

In this article, a simple expression for the center of mass of a system of material points in a two-dimensional surface of Gaussian constant negative curvature is given. By using the basic techniques of geometry, we obtained an expression in intrinsic coordinates, and we showed how this extends the definition for the Euclidean case. The argument is constructive and serves to define the center of mass of a system of particles on the one-dimensional hyperbolic sphere LR1.

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Manin Involutions for Elliptic Pencils and Discrete Integrable Systems

Mathematical Physics Analysis and Geometry ◽

10.1007/s11040-021-09376-4 ◽

2021 ◽

Vol 24 (1) ◽

Author(s):

Matteo Petrera ◽

Yuri B. Suris ◽

Kangning Wei ◽

René Zander

Keyword(s):

Integrable Systems ◽

Geometric Description ◽

Discrete Integrable Systems ◽

Birational Maps ◽

Base Points ◽

Special Geometry ◽

Low Degree ◽

Geometric Study

AbstractWe contribute to the algebraic-geometric study of discrete integrable systems generated by planar birational maps: (a) we find geometric description of Manin involutions for elliptic pencils consisting of curves of higher degree, birationally equivalent to cubic pencils (Halphen pencils of index 1), and (b) we characterize special geometry of base points ensuring that certain compositions of Manin involutions are integrable maps of low degree (quadratic Cremona maps). In particular, we identify some integrable Kahan discretizations as compositions of Manin involutions for elliptic pencils of higher degree.

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