manifestations. See also Introduction to systolic geometry. The systole of a compact metric space X is a metric invariant of X, defined to be the least length...

Systolic geometry is a branch of differential geometry, a field within mathematics, studying problems such as the relationship between the area inside...

the ratio area/sys2. The systolic ratio SR is the reciprocal quantity sys2/area. See also Introduction to systolic geometry. In 1949 Loewner proved his...

Shape of the universe Introduction to the mathematics of general relativity Normal coordinates Systolic geometry Riemann–Cartan geometry in Einstein–Cartan...

differential geometry Synthetic differential geometry Systolic geometry Gauge theory (mathematics) Struik, D. J. "Outline of a History of Differential Geometry: I...

differential geometry, geometric topology, nonstandard analysis, and mathematics education; he is the author of the book Systolic Geometry and Topology...

mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate...

Mathematical Society, ISBN 978-0-8218-3375-9 Katz, Mikhail G. (2007), Systolic geometry and topology, Mathematical Surveys and Monographs, vol. 137, American...

gradient estimates. Gromov made foundational contributions to systolic geometry. Systolic geometry studies the relationship between size invariants (such...

mathematics, Systoles of surfaces are systolic inequalities for curves on surfaces Also see Introduction to systolic geometry This disambiguation page lists...

In the mathematical field of Riemannian geometry, M. Gromov's systolic inequality bounds the length of the shortest non-contractible loop on a Riemannian...

S2CID 123648492. Kitaoka (1993) p. 42 Cassels, J.W.S. (1997). An Introduction to the Geometry of Numbers. Classics in Mathematics (Reprint of 1971 ed.). Springer-Verlag...

about systolic geometry. In 2013, the American Mathematical Society awarded Guth its annual Salem Prize, citing his "major contributions to geometry and...

homotopic to a homothetic covering (Y,g) → (X,g0). Katok's entropy inequality was recently exploited to obtain a tight asymptotic bound for the systolic ratio...

detailed explanation of this viewpoint may be found at the page Introduction to systolic geometry. An alternative formulation of Pu's inequality is the following...

methods. Systolic geometry a branch of differential geometry studying systolic invariants of manifolds and polyhedra. Systolic hyperbolic geometry the study...

(2015). "Instability of a Möbius strip minimal surface and a link with systolic geometry" (PDF). Physical Review Letters. 114 (12): 127801. Bibcode:2015PhRvL...

1090/S0002-9939-97-03692-7. JSTOR 2162098. Katz, Mikhail G. (2007). Systolic geometry and topology. Mathematical Surveys and Monographs. Vol. 137. American...

extend to the more sophisticated context of currents in Kähler manifolds. Gromov's inequality for complex projective space Systolic geometry Federer...

2307/2369402, JSTOR 2369402 Katz, M.; Sabourau, S. (2006). "An optimal systolic inequality for CAT(0) metrics in genus two". Pacific J. Math. 227 (1):...

ingredient in Gromov's inequality for complex projective space in systolic geometry. Closed and exact differential forms Complex differential form Vector-valued...

was not aware of systolic arrays at the time and upon learning the term thought "Oh, that's called a systolic array? It just seemed to make sense." The...

torus, equivalent to D 2 × S 1 . {\displaystyle D^{2}\times S^{1}.} Algebraic topology Alice universe Bavard's Klein bottle systolic inequality Boy's surface...

in large tracts of geometry. Ergodicity results have been provided in translation surfaces, hyperbolic groups and systolic geometry. Techniques include...

death, and LVW thickness greater than 15 mm to 30 mm, on echocardiogram. HCM also presents with a systolic ejection murmur that increases in intensity...

expect larger organisms to be more predisposed to cancer. Pulsus paradoxus: A pulsus paradoxus is an exaggerated decrease in systolic blood pressure during...

05941 [cs.NE]. Minsky M, Papert S (1969). Perceptrons: An Introduction to Computational Geometry. MIT Press. ISBN 978-0-262-63022-1. Bozinovski S. and Fulgosi...

blood pressure, along with the geometry of the aneurysm, researchers can apply computational fluid dynamics (CFD) to predict whether an aneurysm is benign...

1112/plms/s3-13.1.743, MR 0158387 List of University of Waterloo people Systolic geometry In more recent terminology, each impulse would be termed a "bit" with...

has been shown to be equivalent to Power method on a companion matrix for finding eigenvalues. Advancements in systolic arrays have led to a parallelized...