Statement
A student of Charles Loewner's, P.M. Pu proved in a 1950 thesis (published in 1952) that every metric on the real projective plane satisfies the optimal inequality
where sys is the systole. The boundary case of equality is attained precisely when the metric is of constant Gaussian curvature.
Read more about this topic: Pu's Inequality
Famous quotes containing the word statement:
“It is commonplace that a problem stated is well on its way to solution, for statement of the nature of a problem signifies that the underlying quality is being transformed into determinate distinctions of terms and relations or has become an object of articulate thought.”
—John Dewey (1859–1952)
“Eroticism has its own moral justification because it says that pleasure is enough for me; it is a statement of the individual’s sovereignty.”
—Mario Vargas Llosa (b. 1936)
“I think, therefore I am is the statement of an intellectual who underrates toothaches.”
—Milan Kundera (b. 1929)