scholarly journals Inner metric geometry of complex algebraic surfaces with isolated singularities

2008 ◽  
Vol 61 (11) ◽  
pp. 1483-1494 ◽  
Author(s):  
Lev Birbrair ◽  
Alexandre Fernandes
Keyword(s):  
Algebraic Surfaces ◽  
Metric Geometry ◽  
Isolated Singularities ◽  
Inner Metric

Isolated Singularities of Algebraic Surfaces with C ∗ Action

1971 ◽  
Vol 93 (2) ◽  
pp. 205 ◽  
Author(s):  
Peter Orlik ◽  
Philip Wagreich
Keyword(s):  
Algebraic Surfaces ◽  
Isolated Singularities

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.

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