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:
“I am filling the room
with the words from my pen.
Words leak out of it like a miscarriage.
I am zinging words out into the air
and they come back like squash balls.
Yet there is silence.”
—Anne Sexton (1928–1974)
“If you meet a sectary, or a hostile partisan, never recognize the dividing lines; but meet on what common ground remains,—if only that the sun shines, and the rain rains for both; the area will widen very fast, and ere you know it the boundary mountains, on which the eye had fastened, have melted into air.”
—Ralph Waldo Emerson (1803–1882)
“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)