In mathematics, in Riemannian geometry, Mikhail Gromov's filling area conjecture asserts that among all possible fillings of the Riemannian circle of length 2π by a surface with the strongly isometric property, the round hemisphere has the least area. Here the Riemannian circle refers to the unique closed 1-dimensional Riemannian manifold of total 1-volume 2π and Riemannian diameter π.
Read more about Filling Area Conjecture: Explanation, Relation To Pu's Inequality
Famous quotes containing the words filling, area and/or conjecture:
“Oh, but it is dirty!
Mthis little filling station,
oil-soaked, oil-permeated
to a disturbing, over-all
black translucency.
Be careful with that match!”
—Elizabeth Bishop (19111979)
“Whatever an artists personal feelings are, as soon as an artist fills a certain area on the canvas or circumscribes it, he becomes historical. He acts from or upon other artists.”
—Willem De Kooning (b. 1904)
“There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact.”
—Mark Twain [Samuel Langhorne Clemens] (18351910)