The following pages deal with inequalities due to
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Gromov's inequality for complex projective space — In Riemannian geometry, Gromov s optimal stable 2 systolic inequality is the inequality: mathrm{stsys} 2{}^n leq n!;mathrm{vol} {2n}(mathbb{CP}^n),valid for an arbitrary Riemannian metric on the complex projective space, where the optimal bound… … Wikipedia
Gromov's systolic inequality for essential manifolds — In Riemannian geometry, M. Gromov s systolic inequality for essential n manifolds M dates from 1983. It is a lower bound for the volume of an arbitrary metric on M, in terms of its homotopy 1 systole. The homotopy 1 systole is the least length of … Wikipedia
Gromov's theorem — may mean one of a number of results of Mikhail Gromov:*One of Gromov s compactness theorems: ** Gromov s compactness theorem (geometry) in Riemannian geometry ** Gromov s compactness theorem (topology) in symplectic topology *Gromov s Betti… … Wikipedia
Mikhail Leonidovich Gromov — For other people of the same name, see Gromov. Mikhail Leonidovich Gromov Mikhail Gromov Born … Wikipedia
Pu's inequality — [ Roman Surface representing RP2 in R3] In differential geometry, Pu s inequality is an inequality proved by P. M. Pu for the systole of an arbitrary Riemannian metric on the real projective plane RP2.tatementA student of Charles Loewner s, P.M.… … Wikipedia
Bishop–Gromov inequality — In mathematics, the Bishop–Gromov inequality is a classical theorem in Riemannian geometry, named after Richard L. Bishop and Mikhail Gromov. It is the key point in the proof of Gromov s compactness theorem.tatementLet us denote by S^m k a… … Wikipedia
Loewner's torus inequality — In differential geometry, Loewner s torus inequality is an inequality due to Charles Loewner for the systole of an arbitrary Riemannian metric on the 2 torus.tatementIn 1949 Charles Loewner proved that every metric on the 2 torus mathbb T^2… … Wikipedia
Wirtinger inequality (2-forms) — For other inequalities named after Wirtinger, see Wirtinger s inequality. In mathematics, the Wirtinger inequality for 2 forms, named after Wilhelm Wirtinger, states that the exterior scriptstyle uth power of the standard symplectic form omega;,… … Wikipedia
Isoperimetric inequality — The isoperimetric inequality is a geometric inequality involving the square of the circumference of a closed curve in the plane and the area of a plane region it encloses, as well as its various generalizations. Isoperimetric literally means… … Wikipedia
Gaussian isoperimetric inequality — The Gaussian isoperimetric inequality, proved by Boris Tsirelson and Vladimir Sudakov and independently by Christer Borell, states that among all sets of given Gaussian measure in the n dimensional Euclidean space, half spaces have the minimal… … Wikipedia
