OPTIMAL LOWER BOUNDS FOR FIRST EIGENVALUES OF RIEMANN SURFACES FOR LARGE GENUS.

Autor: YUNHUI WU, YUHAO XUE
Předmět:
Zdroj: American Journal of Mathematics; Aug2022, Vol. 144 Issue 4, p1087-1114, 28p
Abstrakt: In this article we study the first eigenvalues of closed Riemann surfaces for large genus. We show that for every closed Riemann surface Xg of genus g (g ≥ 2), the first eigenvalue of Xg is greater than ... up to a uniform positive constant multiplication. Where L1(Xg) is the shortest length of multi closed curves separating Xg. Moreover, we also show that this new lower bound is optimal as g→∞. [ABSTRACT FROM AUTHOR]
Databáze: Complementary Index