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The Propeller: A Counterexample to a Conjectured Criterion for the Existence of Certain Convex Functions
Author(s) -
Kendall Wilfrid S.
Publication year - 1992
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-46.2.364
Subject(s) - counterexample , regular polygon , mathematics , pure mathematics , combinatorics , geometry
A counterexample is given to a conjecture by Emery; it is shown how to construct a domain B (the ‘propeller’) of a two‐dimensional Riemannian manifold such that any pair of points in B is connected by one and only one geodesic in B and yet there is no convex function L : B × B → [0, 1] vanishing only on the diagonal of B × B .