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Area of small disks
Author(s) -
Croke Christopher B.
Publication year - 2009
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdp044
Subject(s) - isoperimetric inequality , mathematics , geodesic , laplace operator , eigenvalues and eigenvectors , upper and lower bounds , zero (linguistics) , radius , mathematical analysis , pure mathematics , linguistics , philosophy , physics , computer security , quantum mechanics , computer science
This paper considers Riemannian metrics on 2‐dimensional disks where all geodesics are minimizing. A sharp reverse isoperimetric inequality is proved. This in turn yields near optimal bounds for the area of disks as well as near optimal upper bounds on the first non‐zero Neumann eigenvalue of the Laplacian in terms only of the radius.