Limits of canonical forms on towers of Riemann surfaces

Research output: Contribution to journal › Journal article › Research › peer-review

Standard

Limits of canonical forms on towers of Riemann surfaces. / Baik, Hyungryul; Shokrieh, Farbod; Wu, Chenxi.

In: Journal fur die Reine und Angewandte Mathematik, Vol. 764, 2020, p. 287-304.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Baik, H, Shokrieh, F & Wu, C 2020, 'Limits of canonical forms on towers of Riemann surfaces', Journal fur die Reine und Angewandte Mathematik, vol. 764, pp. 287-304. https://doi.org/10.1515/crelle-2019-0007

APA

Baik, H., Shokrieh, F., & Wu, C. (2020). Limits of canonical forms on towers of Riemann surfaces. Journal fur die Reine und Angewandte Mathematik, 764, 287-304. https://doi.org/10.1515/crelle-2019-0007

Vancouver

Baik H, Shokrieh F, Wu C. Limits of canonical forms on towers of Riemann surfaces. Journal fur die Reine und Angewandte Mathematik. 2020;764:287-304. https://doi.org/10.1515/crelle-2019-0007

Author

Baik, Hyungryul ; Shokrieh, Farbod ; Wu, Chenxi. / Limits of canonical forms on towers of Riemann surfaces. In: Journal fur die Reine und Angewandte Mathematik. 2020 ; Vol. 764. pp. 287-304.

Bibtex

@article{5a3edc713dde404299c75cc7af470b09,
title = "Limits of canonical forms on towers of Riemann surfaces",
abstract = "We prove a generalized version of Kazhdan's theorem for canonical forms on Riemann surfaces. In the classical version, one starts with an ascending sequence { S n → S } of finite Galois covers of a hyperbolic Riemann surface S, converging to the universal cover. The theorem states that the sequence of forms on S inherited from the canonical forms on S n 's converges uniformly to (a multiple of) the hyperbolic form. We prove a generalized version of this theorem, where the universal cover is replaced with any infinite Galois cover. Along the way, we also prove a Gauss-Bonnet-type theorem in the context of arbitrary infinite Galois covers.",
author = "Hyungryul Baik and Farbod Shokrieh and Chenxi Wu",
year = "2020",
doi = "10.1515/crelle-2019-0007",
language = "English",
volume = "764",
pages = "287--304",
journal = "Journal fuer die Reine und Angewandte Mathematik",
issn = "0075-4102",
publisher = "Walterde Gruyter GmbH",

}

RIS

TY - JOUR

T1 - Limits of canonical forms on towers of Riemann surfaces

AU - Baik, Hyungryul

AU - Shokrieh, Farbod

AU - Wu, Chenxi

PY - 2020

Y1 - 2020

N2 - We prove a generalized version of Kazhdan's theorem for canonical forms on Riemann surfaces. In the classical version, one starts with an ascending sequence { S n → S } of finite Galois covers of a hyperbolic Riemann surface S, converging to the universal cover. The theorem states that the sequence of forms on S inherited from the canonical forms on S n 's converges uniformly to (a multiple of) the hyperbolic form. We prove a generalized version of this theorem, where the universal cover is replaced with any infinite Galois cover. Along the way, we also prove a Gauss-Bonnet-type theorem in the context of arbitrary infinite Galois covers.

AB - We prove a generalized version of Kazhdan's theorem for canonical forms on Riemann surfaces. In the classical version, one starts with an ascending sequence { S n → S } of finite Galois covers of a hyperbolic Riemann surface S, converging to the universal cover. The theorem states that the sequence of forms on S inherited from the canonical forms on S n 's converges uniformly to (a multiple of) the hyperbolic form. We prove a generalized version of this theorem, where the universal cover is replaced with any infinite Galois cover. Along the way, we also prove a Gauss-Bonnet-type theorem in the context of arbitrary infinite Galois covers.

UR - http://www.scopus.com/inward/record.url?scp=85065601746&partnerID=8YFLogxK

U2 - 10.1515/crelle-2019-0007

DO - 10.1515/crelle-2019-0007

M3 - Journal article

AN - SCOPUS:85065601746

VL - 764

SP - 287

EP - 304

JO - Journal fuer die Reine und Angewandte Mathematik

JF - Journal fuer die Reine und Angewandte Mathematik

SN - 0075-4102

ER -

ID: 223822901