Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Introduction_to_systolic_geometry> ?p ?o }
Showing triples 1 to 96 of
96
with 100 triples per page.
- Introduction_to_systolic_geometry abstract "Systolic geometry is a branch of differential geometry, a field within mathematics, studying problems such as the relationship between the area inside a closed curve C, and the length or perimeter of C. Since the area A may be small while the length l is large, when C looks elongated, the relationship can only take the form of an inequality. What is more, such an inequality would be an upper bound for A: there is no interesting lower bound just in terms of the length.Mikhail Gromov once voiced the opinion that the isoperimetric inequality was known already to the Ancient Greeks. The mythological tale of Dido, Queen of Carthage shows that problems about making a maximum area for a given perimeter were posed in a natural way, in past eras.The relation between length and area is closely related to the physical phenomenon known as surface tension, which gives a visible form to the comparable relation between surface area and volume. The familiar shapes of drops of water express minima of surface area.The purpose of this article is to explain another such relation between length and area. A space is called simply connected if every loop in the space can be contracted to a point in a continuous fashion. For example, a room with a pillar in the middle, connecting floor to ceiling, is not simply connected. In geometry, a systole is a distance which is characteristic of a compact metric space which is not simply connected. It is the length of a shortest loop in the space that cannot be contracted to a point in the space. Systolic geometry gives lower bounds for various attributes of the space in terms of its systole.It is known that the Fubini–Study metric is the natural metric for the geometrisation of quantum mechanics. In an intriguing connection to global geometric phenomena, it turns out that the Fubini–Study metric can be characterized as the boundary case of equality in Gromov's inequality for complex projective space, involving an area quantity called the 2-systole, pointing to a possible connection to quantum mechanical phenomena.In the following, these systolic inequalities will be compared to the classical isoperimetric inequalities, which can in turn be motivated by physical phenomena observed in the behavior of a water drop.".
- Introduction_to_systolic_geometry thumbnail Dew_2.jpg?width=300.
- Introduction_to_systolic_geometry wikiPageExternalLink 0803.0690.
- Introduction_to_systolic_geometry wikiPageExternalLink DiffGeom.pdf.
- Introduction_to_systolic_geometry wikiPageID "17669485".
- Introduction_to_systolic_geometry wikiPageLength "13985".
- Introduction_to_systolic_geometry wikiPageOutDegree "59".
- Introduction_to_systolic_geometry wikiPageRevisionID "629061536".
- Introduction_to_systolic_geometry wikiPageWikiLink Algebraic_formula_for_the_variance.
- Introduction_to_systolic_geometry wikiPageWikiLink American_Mathematical_Society.
- Introduction_to_systolic_geometry wikiPageWikiLink Antipodal_map.
- Introduction_to_systolic_geometry wikiPageWikiLink Antipodal_point.
- Introduction_to_systolic_geometry wikiPageWikiLink Area.
- Introduction_to_systolic_geometry wikiPageWikiLink Bonnesens_inequality.
- Introduction_to_systolic_geometry wikiPageWikiLink Category:Systolic_geometry.
- Introduction_to_systolic_geometry wikiPageWikiLink Charles_Loewner.
- Introduction_to_systolic_geometry wikiPageWikiLink Closed_curve.
- Introduction_to_systolic_geometry wikiPageWikiLink Closed_geodesic.
- Introduction_to_systolic_geometry wikiPageWikiLink Closed_surface.
- Introduction_to_systolic_geometry wikiPageWikiLink Communications_on_Pure_and_Applied_Mathematics.
- Introduction_to_systolic_geometry wikiPageWikiLink Compact_set.
- Introduction_to_systolic_geometry wikiPageWikiLink Compact_space.
- Introduction_to_systolic_geometry wikiPageWikiLink Computational_formula_for_the_variance.
- Introduction_to_systolic_geometry wikiPageWikiLink Curve.
- Introduction_to_systolic_geometry wikiPageWikiLink Dido.
- Introduction_to_systolic_geometry wikiPageWikiLink Dido_(Queen_of_Carthage).
- Introduction_to_systolic_geometry wikiPageWikiLink Differential_geometry.
- Introduction_to_systolic_geometry wikiPageWikiLink Eisenstein_integer.
- Introduction_to_systolic_geometry wikiPageWikiLink Eisenstein_integers.
- Introduction_to_systolic_geometry wikiPageWikiLink Essential_manifold.
- Introduction_to_systolic_geometry wikiPageWikiLink Fubinis_theorem.
- Introduction_to_systolic_geometry wikiPageWikiLink Fubini–Study_metric.
- Introduction_to_systolic_geometry wikiPageWikiLink Gaussian_curvature.
- Introduction_to_systolic_geometry wikiPageWikiLink Geometry.
- Introduction_to_systolic_geometry wikiPageWikiLink Girth_(graph_theory).
- Introduction_to_systolic_geometry wikiPageWikiLink Graph_(mathematics).
- Introduction_to_systolic_geometry wikiPageWikiLink Gromovs_inequality_for_complex_projective_space.
- Introduction_to_systolic_geometry wikiPageWikiLink Gromovs_systolic_inequality_for_essential_manifolds.
- Introduction_to_systolic_geometry wikiPageWikiLink Inequality_(mathematics).
- Introduction_to_systolic_geometry wikiPageWikiLink Introduction_to_systolic_geometry.
- Introduction_to_systolic_geometry wikiPageWikiLink Isoperimetric_inequality.
- Introduction_to_systolic_geometry wikiPageWikiLink Loewners_torus_inequality.
- Introduction_to_systolic_geometry wikiPageWikiLink Lusternik–Schnirelmann_category.
- Introduction_to_systolic_geometry wikiPageWikiLink Marcel_Berger.
- Introduction_to_systolic_geometry wikiPageWikiLink Metric_space.
- Introduction_to_systolic_geometry wikiPageWikiLink Mikhail_Gromov_(mathematician).
- Introduction_to_systolic_geometry wikiPageWikiLink Mikhail_Katz.
- Introduction_to_systolic_geometry wikiPageWikiLink Mikhail_Leonidovich_Gromov.
- Introduction_to_systolic_geometry wikiPageWikiLink Notices_of_the_American_Mathematical_Society.
- Introduction_to_systolic_geometry wikiPageWikiLink Pao_Ming_Pu.
- Introduction_to_systolic_geometry wikiPageWikiLink Projective_geometry.
- Introduction_to_systolic_geometry wikiPageWikiLink Pus_inequality.
- Introduction_to_systolic_geometry wikiPageWikiLink Real_projective_plane.
- Introduction_to_systolic_geometry wikiPageWikiLink René_Thom.
- Introduction_to_systolic_geometry wikiPageWikiLink Riemannian_manifold.
- Introduction_to_systolic_geometry wikiPageWikiLink Riemannian_metric.
- Introduction_to_systolic_geometry wikiPageWikiLink Simply_connected.
- Introduction_to_systolic_geometry wikiPageWikiLink Simply_connected_space.
- Introduction_to_systolic_geometry wikiPageWikiLink Surface.
- Introduction_to_systolic_geometry wikiPageWikiLink Surface_area.
- Introduction_to_systolic_geometry wikiPageWikiLink Surface_tension.
- Introduction_to_systolic_geometry wikiPageWikiLink Systoles_of_surfaces.
- Introduction_to_systolic_geometry wikiPageWikiLink Systolic_geometry.
- Introduction_to_systolic_geometry wikiPageWikiLink Systolic_topology.
- Introduction_to_systolic_geometry wikiPageWikiLink Upper_and_lower_bounds.
- Introduction_to_systolic_geometry wikiPageWikiLink Upper_bound.
- Introduction_to_systolic_geometry wikiPageWikiLink Variance.
- Introduction_to_systolic_geometry wikiPageWikiLink Victor_Bangert.
- Introduction_to_systolic_geometry wikiPageWikiLink Volume.
- Introduction_to_systolic_geometry wikiPageWikiLink W._T._Tutte.
- Introduction_to_systolic_geometry wikiPageWikiLink William_Tutte.
- Introduction_to_systolic_geometry wikiPageWikiLink File:Dew_2.jpg.
- Introduction_to_systolic_geometry wikiPageWikiLink File:Steiners_Roman_Surface.gif.
- Introduction_to_systolic_geometry wikiPageWikiLink File:TorusSystoleLoop.png.
- Introduction_to_systolic_geometry wikiPageWikiLinkText "Introduction to systolic geometry".
- Introduction_to_systolic_geometry wikiPageWikiLinkText "Loewner's torus inequality".
- Introduction_to_systolic_geometry wikiPageWikiLinkText "Pu's inequality".
- Introduction_to_systolic_geometry wikiPageWikiLinkText "systole".
- Introduction_to_systolic_geometry hasPhotoCollection Introduction_to_systolic_geometry.
- Introduction_to_systolic_geometry wikiPageUsesTemplate Template:Arxiv.
- Introduction_to_systolic_geometry wikiPageUsesTemplate Template:Introduction.
- Introduction_to_systolic_geometry wikiPageUsesTemplate Template:Systolic_geometry_navbox.
- Introduction_to_systolic_geometry subject Category:Systolic_geometry.
- Introduction_to_systolic_geometry hypernym Branch.
- Introduction_to_systolic_geometry type Article.
- Introduction_to_systolic_geometry type List.
- Introduction_to_systolic_geometry type Organisation.
- Introduction_to_systolic_geometry type Article.
- Introduction_to_systolic_geometry type List.
- Introduction_to_systolic_geometry comment "Systolic geometry is a branch of differential geometry, a field within mathematics, studying problems such as the relationship between the area inside a closed curve C, and the length or perimeter of C. Since the area A may be small while the length l is large, when C looks elongated, the relationship can only take the form of an inequality.".
- Introduction_to_systolic_geometry label "Introduction to systolic geometry".
- Introduction_to_systolic_geometry sameAs Q16146908.
- Introduction_to_systolic_geometry sameAs Q16146908.
- Introduction_to_systolic_geometry wasDerivedFrom Introduction_to_systolic_geometry?oldid=629061536.
- Introduction_to_systolic_geometry depiction Dew_2.jpg.
- Introduction_to_systolic_geometry isPrimaryTopicOf Introduction_to_systolic_geometry.