Degree Theory of Immersed Hypersurfaces

By:

Rosenberg, Harold, 1941- [aut]

Contributor(s):

Smith, Graham [oth]

Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Memoirs of the American Mathematical Society Ser ; no. 1290Publisher: Providence : American Mathematical Society, 2020Description: 1 Online-Ressource (74 p)ISBN:

9781470461485

Subject(s):

Additional physical formats: 147046148X | 1470441853 | 9781470441852 | Erscheint auch als: Degree Theory of Immersed Hypersurfaces. Druck-Ausgabe Providence : American Mathematical Society,c2020DDC classification:

516.3/73

LOC classification:

QA671

Online resources:

Zugang im Netz des KIT

Summary: 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 CoverSummary: 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' formulaSummary: 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 MPPN: PPN: 1755157290Package identifier: Produktsigel: BSZ-4-NLEBK-KAUB | ZDB-4-NLEBK

Holdings ( 0 )

No physical items for this record