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1. www.claymath.org › millennium › poincare-conjecturePoincaré Conjecture - Clay Mathematics Institute

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   24. Mai 2000 · In 1904 the French mathematician Henri Poincaré asked if the three dimensional sphere is characterized as the unique simply connected three manifold. This question, the Poincaré conjecture, was a special case of Thurston's geometrization conjecture. Perelman's proof tells us that every three manifold is built from a set of standard pieces, each with one of eight well-understood geometries.

2. www.science.org › doi › 10The Poincaré Conjecture--Proved | Science

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   22. Dez. 2006 · The third paper, by Huai-Dong Cao of Lehigh University in Bethlehem, Pennsylvania, and Xi-Ping Zhu of Zhongshan University in Guangzhou, China, was less circumspect. Cao and Zhu claimed to have “the first written account of a complete proof of the Poincaré conjecture and the geometrization conjecture of Thurston.” This summer, the ...

3. en.wikipedia.org › wiki › Poincaré_metricPoincaré metric - Wikipedia

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   Poincaré metric. In mathematics, the Poincaré metric, named after Henri Poincaré, is the metric tensor describing a two-dimensional surface of constant negative curvature. It is the natural metric commonly used in a variety of calculations in hyperbolic geometry or Riemann surfaces . There are three equivalent representations commonly used ...

4. www.pks.mpg.de › poincare-recurrencesPoincaré Recurrences - Max Planck Society

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   A beautiful illustration of the Poincaré recurrence theorem was provided by Crutchfield et al. It consists in dynamically evolving (the piexels of) a picture according to a deterministic procedure that corresponds to a Hamiltonian system. A recurrence occurs when the origin image is again obtained. Usually a chaotic system with strong mixing ...

5. www.studysmarter.de › geometrie-studium › poincare-vermutungPoincaré-Vermutung: Erklärung, Bedeutung | StudySmarter

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   Die Poincaré-Vermutung ist eine zentrale Fragestellung der Mathematik, die sich mit der Struktur von Räumen, insbesondere dreidimensionalen Sphären, beschäftigt. Einfach erklärt: Sie besagt, dass ein einfach zusammenhängender, geschlossener 3-dimensionaler Raum homöomorph zu einer 3-dimensionalen Sphäre sein muss.

6. www.universityreview.org › henri-poincare-university-rankingHenri Poincaré University Ranking (University of Lorraine)

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   Henri Poincaré University, in 1996, established a Joint Service Documentation aimed at serving the university community. Included in this project are three university libraries which have materials on the fields of Health, Medicine, Science, Dentistry and Pharmacy. The libraries hold more than 340,000 books, around 2000 electronic theses, and more than 5500 online materials.

7. www.thp.uni-koeln.de › boos_poincare_gauge_theoryPoincaré gauge theory of gravity — An Introduction

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   Poincaré gauge theory of gravity 10/11 After applying the gauge procedure, there are two gauge fields: • the coframe , which is essentially the frame field translational invariance, four parameters field strength: torsion source for torsion: spin-angular momentum • the Lorentz connection , an additional gauge potential