Area, Width, And Logarithmic Capacity Of Convex Sets

Roger Barnard; Kent Pearce; Alexander Solynin

Area, Width, And Logarithmic Capacity Of Convex Sets

Roger Barnard, Kent Pearce, Alexander Solynin

Mathematics and Statistics

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

Abstract

For a planar convex compact set E, we describe the mutual range of its area, width, and logarithmic capacity. This result will follow from a more general theorem describing the mutual range of area, logarithmic capacity, and length of orthogonal projection onto a given axis of an arbitrary compact set, connected or not.

Original language	English
Pages (from-to)	13-23
Journal	Pacific Journal of Mathematics
State	Published - 2003

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title = "Area, Width, And Logarithmic Capacity Of Convex Sets",

abstract = "For a planar convex compact set E, we describe the mutual range of its area, width, and logarithmic capacity. This result will follow from a more general theorem describing the mutual range of area, logarithmic capacity, and length of orthogonal projection onto a given axis of an arbitrary compact set, connected or not.",

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AU - Pearce, Kent

AU - Solynin, Alexander

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AB - For a planar convex compact set E, we describe the mutual range of its area, width, and logarithmic capacity. This result will follow from a more general theorem describing the mutual range of area, logarithmic capacity, and length of orthogonal projection onto a given axis of an arbitrary compact set, connected or not.

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EP - 23

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

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