scholarly journals Statistical regularities of self-intersection counts for geodesics on negatively curved surfaces

2014 ◽  
Vol 163 (6) ◽  
pp. 1191-1261 ◽  
Author(s):  
Steven P. Lalley
Keyword(s):  
Curved Surfaces ◽  
Negatively Curved ◽  
Statistical Regularities

scholarly journals Approximate solutions of cohomological equations associated with some Anosov flows

1990 ◽  
Vol 10 (2) ◽  
pp. 367-379 ◽  
Author(s):  
Svetlana Katok
Keyword(s):  
Approximate Solutions ◽  
Geodesic Flows ◽  
Curved Surfaces ◽  
Anosov Flow ◽  
3 Dimensional ◽  
Negatively Curved ◽  
Anosov Flows ◽  
Higher Differentiability ◽  
Special Case ◽  
Cohomological Equations

AbstractThe Livshitz theorem reported in 1971 asserts that any C1 function having zero integrals over all periodic orbits of a topologically transitive Anosov flow is a derivative of another C1 function in the direction of the flow. Similar results for functions of higher differentiability have also appeared since. In this paper we prove a ‘finite version’ of the Livshitz theorem for a certain class of Anosov flows on 3-dimensional manifolds which include geodesic flows on negatively curved surfaces as a special case.

scholarly journals Local geometry of random geodesics on negatively curved surfaces

2021 ◽  
Vol 4 ◽  
pp. 187-226
Author(s):  
Jayadev Athreya ◽  
Steve Lalley ◽  
Jenya Sapir ◽  
Matthew Wroten
Keyword(s):  
Local Geometry ◽  
Curved Surfaces ◽  
Negatively Curved

scholarly journals Topological uniqueness of negatively curved surfaces

2010 ◽  
Vol 199 ◽  
pp. 137-149
Author(s):  
Hsungrow Chan
Keyword(s):  
Black Hole ◽  
Minimal Surfaces ◽  
Total Curvature ◽  
Second Fundamental Form ◽  
Curved Surfaces ◽  
Index Method ◽  
Negatively Curved ◽  
Asymptotic Curves ◽  
Euclidean Three Space ◽  
Three Space

AbstractIn this paper we consider complete, noncompact, negatively curved surfaces that are twice continuously differentiably embedded in Euclidean three-space, showing that if such surfaces have square integrable second fundamental form, then their topology must, by the index method, be an annulus. We then show how this relates to some minimal surface theorems and has a corollary on minimal surfaces with finite total curvature. In addition, we discuss, by the index method, the relation between the topology and asymptotic curves. Finally, we apply the results yielded to the problem of isometrical immersions into Euclidean three-space of black hole models.

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