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＜電子ブック＞
Liouville-Riemann-Roch Theorems on Abelian Coverings / by Minh Kha, Peter Kuchment
(Lecture Notes in Mathematics. ISSN:16179692 ; 2245)

版	1st ed. 2021.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2021
本文言語	英語
大きさ	XII, 96 p. 2 illus., 1 illus. in color : online resource
著者標目	*Kha, Minh author Kuchment, Peter author SpringerLink (Online service)
件　名	LCSH:Global analysis (Mathematics) LCSH:Manifolds (Mathematics) LCSH:Differential equations FREE:Global Analysis and Analysis on Manifolds FREE:Differential Equations FREE:Manifolds and Cell Complexes
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-030-67428-1

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