Sharp Upper Bound for the First Non-zero Neumann Eigenvalue for Bounded Domains in Rank-1 Symmetric Spaces
نویسندگان
چکیده
In this paper, we prove that for a bounded domain Ω in a rank-1 symmetric space, the first non-zero Neumann eigenvalue μ1(Ω) ≤ μ1(B(r1)) where B(r1) denotes the geodesic ball of radius r1 such that vol(Ω) = vol(B(r1)) and equality holds iff Ω = B(r1). This result generalises the works of Szego, Weinberger and Ashbaugh-Benguria for bounded domains in the spaces of constant curvature.
منابع مشابه
A sharp upper bound for the first eigenvalue of the Laplacian of compact hypersurfaces in rank-1 symmetric spaces
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تاریخ انتشار 1996