scholarly journals The Weil–Petersson metric geometry

2009 ◽  
pp. 47-64 ◽  
Author(s):  
Scott Wolpert
Keyword(s):  
Metric Geometry

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.

On the Metric Geometry of the Plane N-Line

1900 ◽  
Vol 1 (2) ◽  
pp. 97 ◽  
Author(s):  
F. Morley
Keyword(s):  
Metric Geometry

THE WEIERSTRASS E-FUNCTION IN DIFFERENTIAL METRIC GEOMETRY

1933 ◽  
Vol os-4 (1) ◽  
pp. 291-296 ◽  
Author(s):  
J. H. C. WHITEHEAD
Keyword(s):  
Metric Geometry

Fourier Integrals and Metric Geometry

1988 ◽  
pp. 146-171
Author(s):  
J. Von Neumann ◽  
I. J. Schoenberg
Keyword(s):  
Metric Geometry ◽  
Fourier Integrals

The metric geometry of near equilibrium irreversible thermodynamics

1980 ◽  
Vol 72 (5) ◽  
pp. 3127-3129
Author(s):  
Gilbert Nathanson ◽  
Oktay Sinanoğlu
Keyword(s):  
Irreversible Thermodynamics ◽  
Metric Geometry

scholarly journals COARSE COHERENCE OF METRIC SPACES AND GROUPS AND ITS PERMANENCE PROPERTIES

2018 ◽  
Vol 98 (3) ◽  
pp. 422-433
Author(s):  
BORIS GOLDFARB ◽  
JONATHAN L. GROSSMAN
Keyword(s):  
Metric Spaces ◽  
General Context ◽  
Metric Geometry ◽  
Finitely Generated ◽  
Coherence Property ◽  
Finitely Generated Groups ◽  
Permanence Property ◽  
Permanence Properties ◽  
New Framework

We introduce properties of metric spaces and, specifically, finitely generated groups with word metrics, which we call coarse coherence and coarse regular coherence. They are geometric counterparts of the classical algebraic notion of coherence and the regular coherence property of groups defined and studied by Waldhausen. The new properties can be defined in the general context of coarse metric geometry and are coarse invariants. In particular, they are quasi-isometry invariants of spaces and groups. The new framework allows us to prove structural results by developing permanence properties, including the particularly important fibering permanence property, for coarse regular coherence.

Elementary aspects of metric geometry

2010 ◽  
pp. 387-412
Author(s):  
Bennett Chow ◽  
Sun-Chin Chu ◽  
David Glickenstein ◽  
Christine Guenther ◽  
James Isenberg ◽  
...  
Keyword(s):  
Metric Geometry

Thermodynamic metric geometry of the two-state ST2 model for supercooled water

2019 ◽  
Vol 151 (6) ◽  
pp. 064503 ◽  
Author(s):  
Peter Mausbach ◽  
Helge-Otmar May ◽  
George Ruppeiner
Keyword(s):  
Supercooled Water ◽  
Metric Geometry
Sign in / Sign up

Export Citation Format

Share Document