Liouville-Riemann-Roch Theorems on Abelian Coverings
Liouville-Riemann-Roch Theorems on Abelian Coverings (Lecture Notes in Mathematics Book 2245)
by Minh Kha
English | 2021 | ISBN: 3030674274 | 108 Pages | PDF EPUB | 6 MB
by Minh Kha
English | 2021 | ISBN: 3030674274 | 108 Pages | PDF EPUB | 6 MB
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.