Geometry and topology of submanifolds and currents [elektronisk resurs] 2013 Midwest Geometry Conference, October 19, 2013, Oklahoma State University, Stillwater, Oklahoma : 2012 Midwest Geometry Conference, May 12-13, 2012, University of Oklahoma, Norman, Oklahoma / Weiping Li, Shihshu Walter Wei, editors.

• Plateau Problems in Metric Spaces and Related Homology and Cohomology Theories / Robert M. Hardt -- Relating Equivariant and Motivic Cohomology via Analytic Currents / Pedro F. dos Santos, Paulo Lima-Filho, and Robert M. Hardt -- Braids and Symplectic Reidemeister Zeta Functions / Weiping Li -- Systoles of Surfaces and 3-Manifolds / Lizhi Chen and Weiping Li -- Ideal Theory and Classification on Isoparametric Hypersurfaces / Quo-Shin Chi -- The Hartogs Triangle in Complex Analysis / Mei-Chi Shaw -- Finite Volume Flows and Witten’s Deformation / Wenchuan Hu -- On the Existence and Nonexistence of Stable Submanifolds and Currents in Positively Curved Manifolds and the Topology of Submanifolds in Euclidean Spaces / Ralph Howard and Shihshu Walter Wei -- Remarks on Stable Minimal Hypersurfaces in Riemannian Manifolds and Generalized Bernstein Problems / Shihshu Walter Wei, Lina Wu, and Yongsheng Zhang. 

• The papers in this volume are mainly from the 2013 Midwest Geometry Conference, held October 19, 2013, at Oklahoma State University, Stillwater, OK, and partly from the 2012 Midwest Geometry Conference, held May 12-13, 2012, at the University of Oklahoma, Norman, OK. The papers cover recent results on geometry and topology of submanifolds. On the topology side, topics include Plateau problems, Voevodsky's motivic cohomology, Reidemeister zeta function and systolic inequality, and freedom in 2- and 3-dimensional manifolds. On the geometry side, the authors discuss classifying isoparametric hypersurfaces and review Hartogs triangle, finite volume flows, nonexistence of stable p-currents, and a generalized Bernstein type problem. The authors also show that the interaction between topology and geometry is a key to deeply understanding topological invariants and the geometric problems. 

Ämnesord

Submanifolds  -- Congresses (LCSH)

Geometry, Differential  -- Congresses (LCSH)

Commutative algebra  -- Homological methods -- Deformations and infinitesimal methods (msc)

Real functions  -- Polynomials, rational functions -- Polynomials: analytic properties, etc. (msc)

Measure and integration  -- Classical measure theory -- Length, area, volume, other geometric measure theory (msc)

Several complex variables and analytic spaces  -- Complex manifolds -- Positive curvature manifolds (msc)

Several complex variables and analytic spaces  -- Differential operators in several variables -- partial and partial-Neumann operators (msc)

Differential geometry  -- Classical differential geometry -- Minimal surfaces, surfaces with prescribed mean curvature (msc)

Differential geometry  -- Global differential geometry -- Global submanifolds (msc)

Manifolds and cell complexes  -- Low-dimensional topology -- Invariants of knots and 3-manifolds (msc)

Global analysis, analysis on manifolds  -- General theory of differentiable manifolds -- Currents (msc)

Klassifikation

QA649 (LCC)

516.362 (DDC)

13D10 (msc)

14G10 (msc)

14P15 (msc)

26C05 (msc)

28A75 (msc)

32Q10 (msc)

32W05 (msc)

53A10 (msc)

53C40 (msc)

57M27 (msc)

58A25 (msc)

Telf (kssb/8 (machine generated))