| 書目名稱 | Liouville-Riemann-Roch Theorems on Abelian Coverings | | 編輯 | Minh Kha,Peter Kuchment | | 視頻video | http://file.papertrans.cn/587/586827/586827.mp4 | | 概述 | The first unified exposition of Liouville and Riemann–Roch type theorems for elliptic operators on abelian coverings.Gives a well-organized and self-contained exposition of the topic, including new re | | 叢書名稱 | Lecture Notes in Mathematics | | 圖書封面 |  | | 描述 | 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.. | | 出版日期 | Book 2021 | | 關鍵詞 | Abelian Covering; Elliptic Operator; Index Formula; Liouville Theorem; Partial Differential Equations; Pe | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-030-67428-1 | | isbn_softcover | 978-3-030-67427-4 | | isbn_ebook | 978-3-030-67428-1Series ISSN 0075-8434 Series E-ISSN 1617-9692 | | issn_series | 0075-8434 | | copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
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