Limits of canonical forms on towers of Riemann surfaces

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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.
Publisher
WALTER DE GRUYTER GMBH
Issue Date
2020-07
Language
English
Article Type
Article
Citation

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, v.2020, no.764, pp.287 - 304

ISSN
0075-4102
DOI
10.1515/crelle-2019-0007
URI
http://hdl.handle.net/10203/276115
Appears in Collection
MA-Journal Papers(저널논문)
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