東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Liouville-riemann-roch theorems on A...

Kha, Minh.

Linked to FindBook

Google Book

Amazon

博客來

Liouville-riemann-roch theorems on Abelian coverings

Record Type:	Electronic resources : Monograph/item
Title/Author:	Liouville-riemann-roch theorems on Abelian coverings/ by Minh Kha, Peter Kuchment.
Author:	Kha, Minh.
other author:	Kuchment, Peter.
Published:	Cham :Springer International Publishing : : 2021.,
Description:	xii, 96 p. :ill., digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer Nature eBook
Subject:	Differential equations, Elliptic. -
Online resource:	https://doi.org/10.1007/978-3-030-67428-1
ISBN:	9783030674281

Liouville-riemann-roch theorems on Abelian coverings
Kha, Minh.

Liouville-riemann-roch theorems on Abelian coverings[electronic resource] /by Minh Kha, Peter Kuchment. - Cham :Springer International Publishing :2021. - xii, 96 p. :ill., digital ;24 cm. - Lecture notes in mathematics,v.22450075-8434 ;. - Lecture notes in mathematics ;v.2245..

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.

ISBN: 9783030674281

Standard No.: 10.1007/978-3-030-67428-1doiSubjects--Topical Terms:

541859
Differential equations, Elliptic.

LC Class. No.: QA377

Dewey Class. No.: 515.3533

Liouville-riemann-roch theorems on Abelian coverings
LDR:02396nmm a2200337 a 4500 001 2238462
003 DE-He213
005 20210616164831.0
006 m d
007 cr nn 008maaau
008 211111s2021 sz s 0 eng d
020 $a 9783030674281 $q (electronic bk.)
020 $a 9783030674274 $q (paper)
024 7 $a 10.1007/978-3-030-67428-1 $2 doi
035 $a 978-3-030-67428-1
040 $a GP $c GP
041 0 $a eng
050 4 $a QA377
072 7 $a PBKS $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBKS $2 thema
082 0 4 $a 515.3533 $2 23
090 $a QA377 $b .K45 2021
100 1 $a Kha, Minh. $3 3491643
245 1 0 $a Liouville-riemann-roch theorems on Abelian coverings $h [electronic resource] / $c by Minh Kha, Peter Kuchment.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2021.
300 $a xii, 96 p. : $b ill., digital ; $c 24 cm.
490 1 $a Lecture notes in mathematics, $x 0075-8434 ; $v v.2245
505 0 $a 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 $a 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.
650 0 $a Differential equations, Elliptic. $3 541859
650 0 $a Riemann-Roch theorems. $3 706155
650 0 $a Riemannian manifolds. $3 540526
650 1 4 $a Global Analysis and Analysis on Manifolds. $3 891107
650 2 4 $a Analysis. $3 891106
650 2 4 $a Topology. $3 522026
700 1 $a Kuchment, Peter. $3 3491644
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Lecture notes in mathematics ; $v v.2245. $3 3491645
856 4 0 $u https://doi.org/10.1007/978-3-030-67428-1
950 $a Mathematics and Statistics (SpringerNature-11649)