scholarly journals Asymptotic behavior of small eigenvalues, short geodesics and period matrices on degenerating hyperbolic Riemann surfaces

2001 ◽  
Vol 13 (6) ◽  
Author(s):  
J. F. Grotowski ◽  
J. Huntley ◽  
J. Jorgenson
Keyword(s):  
Asymptotic Behavior ◽  
Riemann Surfaces ◽  
Hyperbolic Riemann Surfaces ◽  
Small Eigenvalues

scholarly journals Hyperbolic three-string vertex

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Atakan Hilmi Fırat
Keyword(s):  
Boundary Value Problem ◽  
Conservation Laws ◽  
Riemann Surfaces ◽  
Higher Order ◽  
Local Coordinates ◽  
Pants Decomposition ◽  
Fuchsian Equation ◽  
String Amplitudes ◽  
Hyperbolic Riemann Surfaces ◽  
Liouville’S Equation

Abstract We begin developing tools to compute off-shell string amplitudes with the recently proposed hyperbolic string vertices of Costello and Zwiebach. Exploiting the relation between a boundary value problem for Liouville’s equation and a monodromy problem for a Fuchsian equation, we construct the local coordinates around the punctures for the generalized hyperbolic three-string vertex and investigate their various limits. This vertex corresponds to the general pants diagram with three boundary geodesics of unequal lengths. We derive the conservation laws associated with such vertex and perform sample computations. We note the relevance of our construction to the calculations of the higher-order string vertices using the pants decomposition of hyperbolic Riemann surfaces.

Small eigenvalues on Riemann surfaces of genus 2

1991 ◽  
Vol 106 (1) ◽  
pp. 121-138 ◽  
Author(s):  
Paul Schmutz
Keyword(s):  
Riemann Surfaces ◽  
Genus 2 ◽  
Small Eigenvalues

scholarly journals The homology systole of hyperbolic Riemann surfaces

2011 ◽  
Vol 157 (1) ◽  
pp. 331-338 ◽  
Author(s):  
Hugo Parlier
Keyword(s):  
Riemann Surfaces ◽  
Hyperbolic Riemann Surfaces

BMOA(R, m) and capacity density Bloch spaces on hyperbolic Riemann surfaces

1996 ◽  
Vol 29 (3-4) ◽  
pp. 203-226 ◽  
Author(s):  
Rauno Aulaskari ◽  
Peter Lappan ◽  
Jie Xiao ◽  
Ruhan Zhao
Keyword(s):  
Riemann Surfaces ◽  
Bloch Spaces ◽  
Hyperbolic Riemann Surfaces

Estimating small eigenvalues of Riemann surfaces

1987 ◽  
pp. 93-121 ◽  
Author(s):  
Jozef Dodziuk ◽  
Thea Pignataro ◽  
Burton Randol ◽  
Dennis Sullivan
Keyword(s):  
Riemann Surfaces ◽  
Small Eigenvalues

scholarly journals Banach spaces of bounded solutions of Δu = Pu (P ≥ 0) on hyperbolic riemann surfaces

1974 ◽  
Vol 53 ◽  
pp. 141-155 ◽  
Author(s):  
Mitsuru Nakai
Keyword(s):  
Banach Space ◽  
Riemann Surface ◽  
Banach Spaces ◽  
Riemann Surfaces ◽  
Space Structure ◽  
Bounded Solutions ◽  
Linear Isometry ◽  
Hölder Continuous ◽  
Hyperbolic Riemann Surfaces ◽  
Hyperbolic Riemann Surface

Consider a nonnegative Hölder continuous 2-form P(z)dxdy on a hyperbolic Riemann surface R (z = x + iy). We denote by PB(R) the Banach space of solutions of the equation Δu = Pu on R with finite supremum norms. We are interested in the question how the Banach space structure of PB(R) depends on P. Precisely we consider two such 2-forms P and Q on R and compare PB(R) and QB(R). If there exists a bijective linear isometry T of PB(R) to QB(R), then we say that PB(R) and QB(R) are isomorphic.

Small eigenvalues of Riemann surfaces and graphs

1990 ◽  
Vol 205 (1) ◽  
pp. 395-420 ◽  
Author(s):  
Marc Burger
Keyword(s):  
Riemann Surfaces ◽  
Small Eigenvalues
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