scholarly journals Precise variational formulas for abelian differentials

1980 ◽  
Vol 3 (1) ◽  
pp. 114-143 ◽  
Author(s):  
Akira Yamada
Keyword(s):  
Abelian Differentials ◽  
Variational Formulas

scholarly journals General Variational Formulas for Abelian Differentials

2018 ◽  
Vol 2020 (12) ◽  
pp. 3540-3581 ◽  
Author(s):  
Xuntao Hu ◽  
Chaya Norton
Keyword(s):  
Variational Formula ◽  
Alternative Proof ◽  
Jump Problem ◽  
Period Matrix ◽  
Nodal Curves ◽  
Stable Curve ◽  
Abelian Differentials ◽  
Arbitrary Precision ◽  
Sufficiency Part ◽  
Variational Formulas

AbstractWe use the jump problem technique developed in a recent paper [9] to compute the variational formula of any stable differential and its periods to arbitrary precision in plumbing coordinates. In particular, we give the explicit variational formula for the degeneration of the period matrix, easily reproving the results of Yamada [21] for nodal curves with one node and extending them to an arbitrary stable curve. Concrete examples are included. We also apply the same technique to give an alternative proof of the sufficiency part of the theorem in [1] on the closures of strata of differentials with prescribed multiplicities of zeroes and poles.

Variational Formulas for Higher Affine Mean Curvatures

1988 ◽  
Vol 13 (3-4) ◽  
pp. 318-326 ◽  
Author(s):  
Li An-Min
Keyword(s):  
Variational Formulas

scholarly journals Correction to: Masur–Veech volumes and intersection theory on moduli spaces of Abelian differentials

2021 ◽  
Author(s):  
Dawei Chen ◽  
Martin Möller ◽  
Adrien Sauvaget ◽  
Don Zagier
Keyword(s):  
Moduli Spaces ◽  
Intersection Theory ◽  
Abelian Differentials

A Correction to this paper has been published: https://doi.org/10.1007/s00222-020-00969-4

scholarly journals Extremal Problems for Functions Starlike in the Exterior of the Unit Circle

1962 ◽  
Vol 14 ◽  
pp. 540-551 ◽  
Author(s):  
W. C. Royster
Keyword(s):  
Unit Circle ◽  
Analytic Functions ◽  
Upper Bounds ◽  
Extremal Problems ◽  
Simple Pole ◽  
Image Position ◽  
Inverse Functions ◽  
Variational Formulas

Let Σ represent the class of analytic functions(1)which are regular, except for a simple pole at infinity, and univalent in |z| > 1 and map |z| > 1 onto a domain whose complement is starlike with respect to the origin. Further let Σ- 1 be the class of inverse functions of Σ which at w = ∞ have the expansion(2).In this paper we develop variational formulas for functions of the classes Σ and Σ- 1 and obtain certain properties of functions that extremalize some rather general functionals pertaining to these classes. In particular, we obtain precise upper bounds for |b2| and |b3|. Precise upper bounds for |b1|, |b2| and |b3| are given by Springer (8) for the general univalent case, provided b0 =0.

scholarly journals Compactification of strata of Abelian differentials

2018 ◽  
Vol 167 (12) ◽  
pp. 2347-2416 ◽  
Author(s):  
Matt Bainbridge ◽  
Dawei Chen ◽  
Quentin Gendron ◽  
Samuel Grushevsky ◽  
Martin Möller
Keyword(s):  
Abelian Differentials
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