Gromov's Filling Conjecture
A long-standing open problem, posed by Mikhail Gromov, concerns the calculation of the filling area of the Riemannian circle. The filling area is conjectured to be 2π, a value attained by the hemisphere of constant Gaussian curvature +1.
Read more about this topic: Riemannian Circle
Famous quotes containing the words filling and/or conjecture:
“the gap of today filling itself
as emptiness is distributed
in the idea of what time it is
when that time is already past”
—John Ashbery (b. 1927)
“What these perplexities of my uncle Toby were,—’tis impossible for you to guess;Mif you could,—I should blush ... as an author; inasmuch as I set no small store by myself upon this very account, that my reader has never yet been able to guess at any thing. And ... if I thought you was able to form the least ... conjecture to yourself, of what was to come in the next page,—I would tear it out of my book.”
—Laurence Sterne (1713–1768)