MARC 主機 00000cam  22005897i 4500 
001    1227087123 
003    OCoLC 
005    20210910041927.0 
008    201217t20212021sz a     b    001 0 eng d 
020    9783030674274 
020    3030674274 
024 7  10.1007/978-3-030-67428-1 
035    (OCoLC)1227087123|z(OCoLC)1241658164 
040    YDX|beng|erda|cYDX|dUX0|dQGJ|dLWU|dOCLCF|dKUK|dNHM|dPAU
       |dUKMGB|dAS|dMATH 
050  4 QA3|b.L28 no.2245 
082 04 514.74|223 
100 1  Kha, Minh,|eauthor 
245 10 Liouville-Riemann-Roch theorems on Abelian coverings /
       |cMinh Kha, Peter Kuchment 
264  1 Cham, Switzerland :|bSpringer Nature Switzerland AG,
       |c[2021] 
264  4 |c2021 
300    xii, 93 pages :|bcolor illustration ;|c24 cm 
336    text|btxt|2rdacontent 
337    unmediated|bn|2rdamedia 
338    volume|bnc|2rdacarrier 
490 1  Lecture notes in mathematics,|x0075-8434 ;|vvolume 2245 
504    Includes bibliographical references (pages 87-90) and 
       index 
505 0  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 
520    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 
540    Current copyright fee: GBP19.00|c42\0.|5Uk 
650  0 Topology 
650  0 Differential equations, Elliptic 
650  0 Riemann-Roch theorems 
650  0 Riemannian manifolds 
650  7 Differential equations, Elliptic.|2fast
       |0(OCoLC)fst00893458 
650  7 Riemann-Roch theorems.|2fast|0(OCoLC)fst01097803 
650  7 Riemannian manifolds.|2fast|0(OCoLC)fst01097804 
650  7 Topology.|2fast|0(OCoLC)fst01152692 
700 1  Kuchment, Peter,|d1949-|eauthor 
776 08 |iOnline version:|aKha, Minh.|tLiouville-Riemann-Roch 
       theorems on Abelian coverings.|dCham : Springer, [2021]
       |z9783030674281|w(OCoLC)1237558772 
830  0 Lecture notes in mathematics (Springer-Verlag) ;|v2245 
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