Volume Entropy - Application in Differential Geometry of Surfaces

Application in Differential Geometry of Surfaces

Katok's entropy inequality was recently exploited to obtain a tight asymptotic bound for the systolic ratio of surfaces of large genus, see systoles of surfaces.

Read more about this topic:  Volume Entropy

Famous quotes containing the words application, differential, geometry and/or surfaces:

    “The human mind is capable of excitement without the application of gross and violent stimulants; and he must have a very faint perception of its beauty and dignity who does not know this.”
    —William Wordsworth (1770–1850)

    “But how is one to make a scientist understand that there is something unalterably deranged about differential calculus, quantum theory, or the obscene and so inanely liturgical ordeals of the precession of the equinoxes.”
    —Antonin Artaud (1896–1948)

    “I am present at the sowing of the seed of the world. With a geometry of sunbeams, the soul lays the foundations of nature.”
    —Ralph Waldo Emerson (1803–1882)

    “Footnotes are the finer-suckered surfaces that allow tentacular paragraphs to hold fast to the wider reality of the library.”
    —Nicholson Baker (b. 1957)