作者 Kha, Minh, author
書名 Liouville-Riemann-Roch theorems on Abelian coverings / Minh Kha, Peter Kuchment
出版項 Cham, Switzerland : Springer Nature Switzerland AG, [2021]
2021
國際標準書號 9783030674274
3030674274
國際標準號碼 10.1007/978-3-030-67428-1
book jacket
館藏地 索書號 處理狀態 OPAC 訊息 條碼
 數學所圖書室  QA3 .L28 no.2245    在架上    30340200569345
說明 xii, 93 pages : color illustration ; 24 cm
text txt rdacontent
unmediated n rdamedia
volume nc rdacarrier
系列 Lecture notes in mathematics, 0075-8434 ; volume 2245
Lecture notes in mathematics (Springer-Verlag) ; 2245
附註 Includes bibliographical references (pages 87-90) and index
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
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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鏈接 Online version: Kha, Minh. Liouville-Riemann-Roch theorems on Abelian coverings. Cham : Springer, [2021] 9783030674281 (OCoLC)1237558772
主題 Topology
Differential equations, Elliptic
Riemann-Roch theorems
Riemannian manifolds
Differential equations, Elliptic. fast (OCoLC)fst00893458
Riemann-Roch theorems. fast (OCoLC)fst01097803
Riemannian manifolds. fast (OCoLC)fst01097804
Topology. fast (OCoLC)fst01152692
Alt Author Kuchment, Peter, 1949- author