Opening infinitely many nodes
Martin Traizet
TL;DR
This paper develops a theory of holomorphic differentials on a class of non-compact Riemann surfaces created by opening infinitely many nodes, expanding understanding of complex structures on such surfaces.
Contribution
It introduces a new theoretical framework for holomorphic differentials on non-compact Riemann surfaces with infinitely many nodes, a novel class of geometric objects.
Findings
Established foundational properties of holomorphic differentials on these surfaces.
Provided methods to analyze complex structures on infinitely connected Riemann surfaces.
Extended classical theories to a new class of non-compact surfaces.
Abstract
We develop a theory of holomorphic differentials on a certain class of non-compact Riemann surfaces obtained by opening infinitely many nodes.
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Taxonomy
TopicsGeometry and complex manifolds · Holomorphic and Operator Theory · Geometric Analysis and Curvature Flows