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From Fourier Analysis and Number Theory to Radon Transforms and Geometry pp 303–324Cite as

Some Intrinsic Constructions on Compact Riemann Surfaces

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Part of the book series: Developments in Mathematics ((DEVM,volume 28))

Abstract

For any prescribed differential principal part on a compact Riemann surface, there are uniquely determined and intrinsically defined meromorphic abelian differentials with these principal parts, defined independently of any choice of a marking of the surface or of a basis for the holomorphic abelian differentials, and they are holomorphic functions of the singularities. They can be constructed explicitly in terms of intrinsically defined cross-ratio functions on the Riemann surfaces, the classical cross-ratio function for the Riemann sphere, and natural generalizations for surfaces of higher genus.

Mathematics Subject Classification (2010): 30F10 (Primary), 30F30, 14H55

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Author information

Authors and Affiliations

  1. Fine Hall, Princeton University, Princeton, NJ, USA

    Robert C. Gunning

Authors
  1. Robert C. Gunning
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Correspondence to Robert C. Gunning .

Editor information

Editors and Affiliations

  1. , Einstein Institute of Mathematics, Hebrew University of Jerusalem, Jerusalem, 91904, Israel

    Hershel M. Farkas

  2. , Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, 08544, New Jersey, USA

    Robert C. Gunning

  3. , Department of Mathematics, Temple University, Wachman Hall 608, Philadelphia, 19122, Pennsylvania, USA

    Marvin I. Knopp

  4. , Department of Mathematics, University of Michigan, Church St. 530, Ann Arbor, 48109, Michigan, USA

    B. A. Taylor

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Gunning, R.C. (2013). Some Intrinsic Constructions on Compact Riemann Surfaces. In: Farkas, H., Gunning, R., Knopp, M., Taylor, B. (eds) From Fourier Analysis and Number Theory to Radon Transforms and Geometry. Developments in Mathematics, vol 28. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4075-8_13

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