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The Szegö–Weinberger inequality asserts that the second Neumann eigenvalue $$\mu _2$$μ2 of Laplace operator on a bounded domain in $$\mathbb {R}^n$$Rn is bounded from above by that of a ball… Click to show full abstract
The Szegö–Weinberger inequality asserts that the second Neumann eigenvalue $$\mu _2$$μ2 of Laplace operator on a bounded domain in $$\mathbb {R}^n$$Rn is bounded from above by that of a ball of the same volume. In this note, we prove an upper bound for $$\mu _2$$μ2 on domains in Riemannian manifolds, which can be viewed as a Sezgö–Weinberger type inequality.
Keywords:
bound second;
neumann eigenvalue;
riemannian manifolds;
upper bound;
second neumann;
eigenvalue riemannian
Journal Title: Geometriae Dedicata
Year Published: 2019
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Journal Title: Geometriae Dedicata
Year Published: 2019
Link to full text (if available)
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recommendations!