Geometry and Topology of Submanifolds and Currents

Geometry and Topology of Submanifolds and Currents

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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.
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Product details

  • Paperback | 186 pages
  • 178 x 254 x 19.05mm | 294.84g
  • Providence, United States
  • English
  • 1470415569
  • 9781470415563

Table of contents

Plateau problems in metric spaces and related homology and cohomology theories by R. M. Hardt
Relating equivariant and motivic cohomology via analytic currents by P. F. dos Santos, P. Lima-Filho, and R. M. Hardt
Braids and symplectic Reidemeister zeta functions by W. Li
Systoles of surfaces and 3-manifolds by L. Chen and W. Li
Ideal theory and classification of isoparametric hypersurfaces by Q.-S. Chi
The Hartogs triangle in complex analysis by M.-C. Shaw
Finite volume flows and Witten's deformation by W. Hu
On the existence and nonexistence of stable submanifolds and currents in positively curved manifolds and the topology of submanifolds in Euclidean spaces by R. Howard and W. Wei
Remarks on stable minimal hypersurfaces in Riemannian manifolds and generalized Bernstein problems by S. W. Wei, L. Wu, and Y. Zhang
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About Weiping Li

Weiping Li, Southwest Jiaotong University, Chengdu, Sichuan Province, People's Republic of China, and Oklahoma State University, Stillwater, OK, USA.

Shihshu Walter Wei, University of Oklahoma, Norman, OK, USA.
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