說明 
xii, 93 pages : color illustration ; 24 cm 

text txt rdacontent 

unmediated n rdamedia 

volume nc rdacarrier 
系列 
Lecture notes in mathematics, 00758434 ; volume 2245


Lecture notes in mathematics (SpringerVerlag) ; 2245

附註 
Includes bibliographical references (pages 8790) and index 

This book is devoted to computing the index of elliptic PDEs on noncompact 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 nontrivial. 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 LiouvilleRiemannRoch Theorems  Auxiliary Statements and Proofs of Technical Lemmas  Final Remarks and Conclusions 

Current copyright fee: GBP19.00 42\0. Uk 
鏈接 
Online version: Kha, Minh. LiouvilleRiemannRoch theorems on Abelian coverings.
Cham : Springer, [2021] 9783030674281
(OCoLC)1237558772

主題 
Topology


Differential equations, Elliptic


RiemannRoch theorems


Riemannian manifolds


Differential equations, Elliptic. fast (OCoLC)fst00893458


RiemannRoch theorems. fast (OCoLC)fst01097803


Riemannian manifolds. fast (OCoLC)fst01097804


Topology. fast (OCoLC)fst01152692

Alt Author 
Kuchment, Peter, 1949 author

