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13 relations: American Mathematical Society, Complex projective space, Duke Mathematical Journal, Fubini–Study metric, Gromov's inequality, Gromov's systolic inequality for essential manifolds, Loewner's torus inequality, Mikhail Leonidovich Gromov, Pu's inequality, Quantum mechanics, Riemannian geometry, Systolic geometry, Wirtinger inequality (2-forms).
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.
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Complex projective space
In mathematics, complex projective space is the projective space with respect to the field of complex numbers.
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Duke Mathematical Journal
Duke Mathematical Journal is a peer-reviewed mathematics journal published by Duke University Press.
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Fubini–Study metric
In mathematics, the Fubini–Study metric is a Kähler metric on projective Hilbert space, that is, on a complex projective space CPn endowed with a Hermitian form.
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Gromov's inequality
The following pages deal with inequalities due to Mikhail Gromov.
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Gromov's systolic inequality for essential manifolds
In the mathematical field of Riemannian geometry, M. Gromov's systolic inequality bounds the length of the shortest non-contractible loop on a Riemannian manifold in terms of the volume of the manifold.
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Loewner's torus inequality
In differential geometry, Loewner's torus inequality is an inequality due to Charles Loewner.
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Mikhail Leonidovich Gromov
Mikhail Leonidovich Gromov (also Mikhael Gromov, Michael Gromov or Mischa Gromov; Михаи́л Леони́дович Гро́мов; born 23 December 1943), is a French-Russian mathematician known for work in geometry, analysis and group theory.
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Pu's inequality
In differential geometry, Pu's inequality, proved by Pao Ming Pu, relates the area of an arbitrary Riemannian surface homeomorphic to the real projective plane with the lengths of the closed curves contained in it.
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Quantum mechanics
Quantum mechanics (QM; also known as quantum physics, quantum theory, the wave mechanical model, or matrix mechanics), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.
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Riemannian geometry
Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a Riemannian metric, i.e. with an inner product on the tangent space at each point that varies smoothly from point to point.
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Systolic geometry
In mathematics, systolic geometry is the study of systolic invariants of manifolds and polyhedra, as initially conceived by Charles Loewner and developed by Mikhail Gromov, Michael Freedman, Peter Sarnak, Mikhail Katz, Larry Guth, and others, in its arithmetical, ergodic, and topological manifestations.
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Wirtinger inequality (2-forms)
In mathematics, the Wirtinger inequality for 2-forms, named after Wilhelm Wirtinger, states that on a Kähler manifold M, the exterior kth power of the symplectic form (Kähler form) ω, when evaluated on a simple (decomposable) (2k)-vector ζ of unit volume, is bounded above by k!.
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References
[1] https://en.wikipedia.org/wiki/Gromov's_inequality_for_complex_projective_space
