TY  - BOOK
AU  - Rosenberg,Harold
AU  - Smith,Graham
TI  - Degree Theory of Immersed Hypersurfaces
T2  - Memoirs of the American Mathematical Society Series
SN  - 9781470461485
AV  - QA671 .R674 2020 
U1  - 516.3/73 
PY  - 2020///
CY  - Providence
PB  - American Mathematical Society
KW  - Topological degree
KW  - Riemannian manifolds
KW  - Hypersurfaces
KW  - Curvature
KW  - Electronic books
N1  - Cover -- Title page -- Chapter 1. Introduction -- 1.1. General -- 1.2. Background -- 1.3. Applications -- Acknowledgments -- Chapter 2. Degree theory -- 2.1. The manifold of immersions and its tangent bundle -- 2.2. Curvature as a vector field -- 2.3. Simplicity -- 2.4. Surjectivity -- 2.5. Finite dimensional sections -- 2.6. Extensions -- 2.7. Orientation - the finite-dimensional case -- 2.8. Orientation - the infinite-dimensional case -- 2.9. Constructing the degree -- 2.10. Varying the metric -- Chapter 3. Applications -- 3.1. The generalised Simons' formula -- 3.2. Prescribed mean curvature -- 3.3. Calculating the Degree -- 3.4. Extrinstic Curvature -- 3.5. Special Lagrangian curvature -- 3.6. Extrinsic curvature in two dimensions -- Appendix A. Weakly smooth maps -- Appendix B. Prime immersions -- Bibliography -- Back Cover
N2  - The authors develop a degree theory for compact immersed hypersurfaces of prescribed K-curvature immersed in a compact, orientable Riemannian manifold, where K is any elliptic curvature function. They apply this theory to count the (algebraic) number of immersed hyperspheres in various cases: where K is mean curvature, extrinsic curvature and special Lagrangian curvature and show that in all these cases, this number is equal to -\chi(M), where \chi(M) is the Euler characteristic of the ambient manifold M
UR  - https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=6229940
ER  -