arXiv subjects

Binoy

Publications and source records attributed to Binoy.

2 recordsLinked to original sources

arXiv2013

Sharp upper bound for the first eigenvalue

Let $M$ be a closed hypersurface in a noncompact rank-1 symmetric space $(\bar{\mathbb{M}}, ds^2)$ with $-4 \leq K_{\bar{\mathbb{M}}} \leq -1,$ or in a complete, simply connected Riemannian manifold $\mathbb{M}$ such that $0 \leq K_{\mathbb{M}} \leq δ^2$ or $K_{\mathbb{M}} \leq k$ where $k = -δ^2$ or 0. In this paper we give sharp upperbounds for the first eigenvalue of laplacian of $M$.

math.DG↗

arXiv2012

Sharp upper bound and a comparison theorem for the first nonzero Steklov eigenvalue

In this paper we prove that given a volume, among all domains with smooth boundary in rank-1 symmetric spaces of noncompact type, geodesic balls maximizes the first nonzero Steklov eigenvalue. We also prove a comparison result for the first nonzero Steklov eigenvalue for domains in simply connected Riemannian manifolds with certain curvature bounds.

math.DG↗