A sharp upper bound for the first Dirichlet eigenvalue of cone-like domains
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DOI: 10.1007/s00013-020-01499-4
Abstract: The aim of this paper is to give a complementary upper bound-type isoperimetric inequality for the fundamental Dirichlet eigenvalue of a bounded domain completely contained in a cone. This inequality is a counterpart to the… read more here.
Keywords: inequality; dirichlet eigenvalue; sharp upper; upper bound ... See more keywords
Sharp upper diameter bounds for compact shrinking Ricci solitons
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DOI: 10.1007/s10455-021-09764-7
Abstract: We give a sharp upper diameter bound for a compact shrinking Ricci soliton in terms of its scalar curvature integral and the Perelman's entropy functional. The sharp cases could occur at round spheres. The proof… read more here.
Keywords: compact shrinking; ricci solitons; shrinking ricci; upper diameter ... See more keywords
A sharp upper bound for the 2‐torsion of class groups of multiquadratic fields
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DOI: 10.1112/mtk.12123
Abstract: Let $K$ be a multiquadratic extension of $\mathbb{Q}$ and let $\text{Cl}^{+}(K)$ be its narrow class group. Recently, the authors \cite{KP} gave a bound for $|\text{Cl}^{+}(K)[2]|$ only in terms of the degree of $K$ and the… read more here.
Keywords: bound torsion; class; upper bound; class groups ... See more keywords