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Geometry and Topology of Submanifolds and Currents
About this Title
Weiping Li, Oklahoma State University, Stillwater, OK and Shihshu Walter Wei, University of Oklahoma, Norman, OK, Editors
Publication: Contemporary Mathematics
Publication Year: 2015; Volume 646
ISBNs: 978-1-4704-1556-3 (print); 978-1-4704-2669-9 (online)
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.
Graduate students and research mathematicians interested in geometry and topology.
Table of Contents
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- Robert M. Hardt – Plateau Problems in Metric Spaces and Related Homology and Cohomology Theories
- Pedro F. dos Santos, Paulo Lima-Filho and Robert M. Hardt – Relating Equivariant and Motivic Cohomology via Analytic Currents
- Weiping Li – Braids and Symplectic Reidemeister Zeta Functions
- Lizhi Chen and Weiping Li – Systoles of Surfaces and $3$-Manifolds
- Quo-Shin Chi – Ideal Theory and Classification of Isoparametric Hypersurfaces
- Mei-Chi Shaw – The Hartogs Triangle in Complex Analysis
- Wenchuan Hu – Finite Volume Flows and Witten’s Deformation
- Ralph Howard and Shihshu Walter Wei – On the Existence and Nonexistence of Stable Submanifolds and Currents in Positively Curved Manifolds and the Topology of Submanifolds in Euclidean Spaces
- Shihshu Walter Wei, Lina Wu and Yongsheng Zhang – Remarks on Stable Minimal Hypersurfaces in Riemannian Manifolds and Generalized Bernstein Problems