Liouville-Riemann-Roch theorems on abelian coverings

29 Sep 2019 Kha Minh Kuchment Peter

The classical Riemann-Roch theorem has been extended by N. Nadirashvili and then M. Gromov and M. Shubin to computing indices of elliptic operators on compact (as well as non-compact) manifolds, when a divisor mandates a finite number of zeros and allows a finite number of poles of solutions. On the other hand, Liouville type theorems count the number of solutions that are allowed to have a "pole at infinity.".. (read more)

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