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  2. Poincaré inequality - Wikipedia

    en.wikipedia.org/wiki/Poincaré_inequality

    In the context of metric measure spaces, the definition of a Poincaré inequality is slightly different.One definition is: a metric measure space supports a (q,p)-Poincare inequality for some , < if there are constants C and λ ≥ 1 so that for each ball B in the space, ‖ ‖ ⁡ () ‖ ‖ ().

  3. Henri Poincaré - Wikipedia

    en.wikipedia.org/wiki/Henri_Poincaré

    Jules Henri Poincaré (UK: / ˈ p w æ̃ k ɑːr eɪ /, US: / ˌ p w æ̃ k ɑː ˈ r eɪ /; French: [ɑ̃ʁi pwɛ̃kaʁe] ⓘ; [1] 29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science.

  4. Poincaré group - Wikipedia

    en.wikipedia.org/wiki/Poincaré_group

    The Poincaré group consists of all coordinate transformations of Minkowski space that do not change the spacetime interval between events.For example, if everything were postponed by two hours, including the two events and the path you took to go from one to the other, then the time interval between the events recorded by a stopwatch that you carried with you would be the same.

  5. Poincaré metric - Wikipedia

    en.wikipedia.org/wiki/Poincaré_metric

    J-invariant in Poincare disk coordinates; note this disk is rotated by 90 degrees from canonical coordinates given in this article. A second common mapping of the upper half-plane to a disk is the q-mapping = ⁡ where q is the nome and τ is the half-period ratio:

  6. Friedrichs's inequality - Wikipedia

    en.wikipedia.org/wiki/Friedrichs's_inequality

    In mathematics, Friedrichs's inequality is a theorem of functional analysis, due to Kurt Friedrichs. It places a bound on the L p norm of a function using L p bounds on the weak derivatives of the function and the geometry of the domain , and can be used to show that certain norms on Sobolev spaces are equivalent.

  7. Sobolev space - Wikipedia

    en.wikipedia.org/wiki/Sobolev_space

    In the one-dimensional case the Sobolev space , for is defined as the subset of functions in () such that and its weak derivatives up to order have a finite L p norm.As mentioned above, some care must be taken to define derivatives in the proper sense.

  8. Poincaré conjecture - Wikipedia

    en.wikipedia.org/wiki/Poincaré_conjecture

    In the mathematical field of geometric topology, the Poincaré conjecture (UK: / ˈ p w æ̃ k ær eɪ /, [2] US: / ˌ p w æ̃ k ɑː ˈ r eɪ /, [3] [4] French: [pwɛ̃kaʁe]) is a theorem about the characterization of the 3-sphere, which is the hypersphere that bounds the unit ball in four-dimensional space.

  9. Raymond Poincaré - Wikipedia

    en.wikipedia.org/wiki/Raymond_Poincaré

    Poincaré, Raymond, The memoirs of Raymond Poincare 1912 (1926) online; Poincaré, Raymond, The Memoirs Of Raymond Poincare 1913-1914 (1928) online; Poincaré, Raymond, In the Service of France: The Day After Agadir, 1912 (Vol. I) online , in French; Poincaré, Raymond, In the Service of France: The Balkans on Fire, 1912 (Vol. II) online , in ...