The inradius, the irst eigenvalue and the torsional rigidity of curvilinear polygons

Alexander Solynin; Victor A. Zalgaller

The inradius, the irst eigenvalue and the torsional rigidity of curvilinear polygons

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we prove several inequalities for the first eigenvalue, torsional rigidity, and the inradius for curvilinear polygons with n sides, each of which is a smooth arc of a bounded curvature. Our main proofs rely on the method of dissymmetrization and on a special geometrical containment theorem for curvilinear polygons.

Original language	English
Pages (from-to)	765-783
Journal	Bulletin of the London Mathematical Society
State	Published - Oct 2010

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abstract = "In this paper, we prove several inequalities for the first eigenvalue, torsional rigidity, and the inradius for curvilinear polygons with n sides, each of which is a smooth arc of a bounded curvature. Our main proofs rely on the method of dissymmetrization and on a special geometrical containment theorem for curvilinear polygons.",

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AU - Zalgaller, Victor A.

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N2 - In this paper, we prove several inequalities for the first eigenvalue, torsional rigidity, and the inradius for curvilinear polygons with n sides, each of which is a smooth arc of a bounded curvature. Our main proofs rely on the method of dissymmetrization and on a special geometrical containment theorem for curvilinear polygons.

AB - In this paper, we prove several inequalities for the first eigenvalue, torsional rigidity, and the inradius for curvilinear polygons with n sides, each of which is a smooth arc of a bounded curvature. Our main proofs rely on the method of dissymmetrization and on a special geometrical containment theorem for curvilinear polygons.

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EP - 783

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

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