Let I be a simply-connected complete d-dimensional Riemannian manifold of nonpositive sectional curvature K.If K≦– k2<0, then the infimum of the L2spectrum of the negative Laplacian is greater than or equal to (d–1)2K2/4 with equality in case K⟶–k2sufficiently fast at infinity.This general result is obtained by analyzing a system of ordinary differential equations. If either d=2 or the manifold possesses appropriate symmetry, the result is obtained under weaker conditions by analyzing a Riccati equation.Finally the case k=0 is treated separately.
|Original language||English (US)|
|Number of pages||8|
|Journal||Pacific Journal of Mathematics|
|State||Published - May 1981|
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