Lecture Notes in Mathematics

Liouville-Riemann-Roch Theorems on Abelian Coverings

Authors: Kha, Minh, Kuchment, Peter

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  • The first unified exposition of Liouville and Riemann–Roch type theorems for elliptic operators on abelian coverings
  • Gives a well-organized and self-contained exposition of the topic, including new results
  • Intersects with geometric analysis, the spectral theory of periodic operators, and their applications
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eBook 37,44 €
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  • ISBN 978-3-030-67428-1
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Softcover 46,79 €
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  • ISBN 978-3-030-67427-4
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About this book

This book is devoted to computing the index of elliptic PDEs on non-compact Riemannian manifolds in the presence of local singularities and zeros, as well as polynomial growth at infinity. The classical Riemann–Roch theorem and its generalizations to elliptic equations on bounded domains and compact manifolds, due to Maz’ya, Plameneskii, Nadirashvilli, Gromov and Shubin, account for the contribution to the index due to a divisor of zeros and singularities. On the other hand, the Liouville theorems of Avellaneda, Lin, Li, Moser, Struwe, Kuchment and Pinchover provide the index of periodic elliptic equations on abelian coverings of compact manifolds with polynomial growth at infinity, i.e. in the presence of a "divisor" at infinity.
A natural question is whether one can combine the Riemann–Roch and Liouville type results. This monograph shows that this can indeed be done, however the answers are more intricate than one might initially expect. Namely, the interaction between the finite divisor and the point at infinity is non-trivial.
The text is targeted towards researchers in PDEs, geometric analysis, and mathematical physics.

Table of contents (5 chapters)

Table of contents (5 chapters)

Buy this book

eBook 37,44 €
price for Spain (gross)
  • ISBN 978-3-030-67428-1
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 46,79 €
price for Spain (gross)
  • ISBN 978-3-030-67427-4
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Liouville-Riemann-Roch Theorems on Abelian Coverings
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2245
Copyright
2021
Publisher
Springer International Publishing
Copyright Holder
The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
eBook ISBN
978-3-030-67428-1
DOI
10.1007/978-3-030-67428-1
Softcover ISBN
978-3-030-67427-4
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XII, 96
Number of Illustrations
1 b/w illustrations, 1 illustrations in colour
Topics