Limits of canonical forms on towers of Riemann surfaces
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- OA-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.
Original language | English |
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Journal | Journal fur die Reine und Angewandte Mathematik |
Volume | 764 |
Pages (from-to) | 287-304 |
ISSN | 0075-4102 |
DOIs | |
Publication status | Published - 2020 |
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