Liouville-Riemann-Roch theorems on Abelian coverings / Minh Kha, Peter Kuchment.
Kha, Minh, author.; Kuchment, Peter, 1949- author.
2021
QA377
Available Online

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Title Liouville-Riemann-Roch theorems on Abelian coverings / Minh Kha, Peter Kuchment.
Author Kha, Minh, author.
ISBN 9783030674281 (electronic bk.)
3030674282 (electronic bk.)
3030674274
9783030674274
DOI https://doi.org/10.1007/978-3-030-67428-1
Published Cham : Springer, [2021]
Language English
Description 1 online resource
Item Number 10.1007/978-3-030-67428-1 doi
Call Number QA377
Dewey Decimal Classification 515/.3533
Summary 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 RiemannRoch theorem and its generalizations to elliptic equations on bounded domains and compact manifolds, due to Mazya, 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 RiemannRoch 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
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Digital File Characteristics text file
PDF
Source of Description Online resource; title from PDF title page (SpringerLink, viewed March 17, 2021).
Added Author Kuchment, Peter, 1949- author.
Series Lecture notes in mathematics (Springer-Verlag) ; 2245.
Available in Other Form Print version: 9783030674274
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Preliminaries
The Main Results
Proofs of the Main Results
Specific Examples of Liouville-Riemann-Roch Theorems
Auxiliary Statements and Proofs of Technical Lemmas
Final Remarks and Conclusions.

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