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:
“It is a secret from nobody that the famous random event is most likely to arise from those parts of the world where the old adage “There is no alternative to victory” retains a high degree of plausibility.”
—Hannah Arendt (1906–1975)
“You do not mean by mystery what a Catholic does. You mean an interesting uncertainty: the uncertainty ceasing interest ceases also.... But a Catholic by mystery means an incomprehensible certainty: without certainty, without formulation there is no interest;... the clearer the formulation the greater the interest.”
—Gerard Manley Hopkins (1844–1889)