**Contemporary Mathematics**

Volume: 646;
2015;
186 pp;
Softcover

MSC: Primary 13; 14; 26; 28; 32; 53; 57; 58;

**Print ISBN: 978-1-4704-1556-3
Product Code: CONM/646**

List Price: $112.00

AMS Member Price: $89.60

MAA Member Price: $100.80

**Electronic ISBN: 978-1-4704-2669-9
Product Code: CONM/646.E**

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# Geometry and Topology of Submanifolds and Currents

Share this page *Edited by *
*Weiping Li; Shihshu Walter Wei*

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.

#### Readership

Graduate students and research mathematicians interested in geometry and topology.

# Table of Contents

## Geometry and Topology of Submanifolds and Currents

- Cover Cover11 free
- Title page iii4 free
- Contents v6 free
- Preface vii8 free
- 2013 Midwest Geometry Conference (MGC XIX) Talks ix10 free
- Plateau Problems in Metric Spaces and Related Homology and Cohomology Theories 112 free
- Relating Equivariant and Motivic Cohomology via Analytic Currents 1930
- Braids and Symplectic Reidemeister Zeta Functions 4152
- Systoles of Surfaces and 3-Manifolds 6172
- Ideal Theory and Classification of Isoparametric Hypersurfaces 8192
- The Hartogs Triangle in Complex Analysis 105116
- Finite Volume Flows and Witten’s Deformation 117128
- On the Existence and Nonexistence of Stable Submanifolds and Currents in Positively Curved Manifolds and the Topology of Submanifolds in Euclidean Spaces 127138
- 1. Introduction 128139
- 2. Universally mass decreasing sets of vector fields 132143
- 3. Trace formulas for immersed submanifolds of Euclidean Space 137148
- 4. Applications to the topology of hypersurfaces 143154
- 5. Topological vanishing theorems for submanifolds of Euclidean space 146157
- 6. Stable currents in the rank one symmetric spaces 154165
- 7. Mass minimizing currents modulo two in real projective spaces 160171
- 8. The Topology of noncompact stable hypersurfaces in Riemannian manifolds 162173
- Acknowledgment 165176
- References 165176

- Remarks on Stable Minimal Hypersurfaces in Riemannian Manifolds and Generalized Bernstein Problems 169180
- 1. Introduction 169180
- 2. Preliminaries 173184
- 3. Stable Minimal Hypersurfaces 174185
- 4. Generalized Bernstein Problems 177188
- 5. Dualities 180191
- 6. The Unity 182193
- 7. The case 𝑝=0: Meeting 𝐠 “head on” Without Making a Conformal Change 183194
- 8. The Case 𝑝∈(2-2/𝑛,∞): Some Interplays Between 𝑅 and 𝑅 184195
- 9. The Rigidity of Stable Minimal Hypersurfaces 185196
- Acknowledgement 185196
- References 185196

- Back Cover Back Cover1200