Alternative Formulation
Given a doubly periodic metric on (e.g. an imbedding in which is invariant by a isometric action), there is a nonzero element and a point such that, where is a fundamental domain for the action, while is the Riemannian distance, namely least length of a path joining and .
Read more about this topic: Loewner's Torus Inequality
Famous quotes containing the words alternative and/or formulation:
“If you have abandoned one faith, do not abandon all faith. There is always an alternative to the faith we lose. Or is it the same faith under another mask?”
—Graham Greene (19041991)
“In necessary things, unity; in disputed things, liberty; in all things, charity.”
—Variously Ascribed.
The formulation was used as a motto by the English Nonconformist clergyman Richard Baxter (1615-1691)