Degree theory of immersed hypersurfaces / Harold Rosenberg, Graham Smith.

Format:

Book

Author/Creator:

Rosenberg, H. (Harold), 1941- author.

Smith, Graham (Graham Andrew Craig), author.

Series:

Memoirs of the American Mathematical Society ; no. 1290.

Memoirs of the American Mathematical Society, 0065-9266 ; number 1290

Language:

English

Subjects (All):

Riemannian manifolds.

Topological degree.

Hypersurfaces.

Curvature.

Physical Description:

v, 62 pages : illustrations ; 26 cm.

Place of Publication:

Providence, RI : American Mathematical Society, 2020.

Summary:

"We 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. We 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 we show that in all these cases, this number is equal to -χ(M), where χ(M) is the Euler characteristic of the ambient manifold M"-- Provided by publisher.

Contents:

Degree theory

Applications.

Notes:

Includes bibliographical references.

"May 2020, volume 265, number 1290 (seventh of 7 numbers)."

ISBN:

9781470441852

1470441853

OCLC:

1151815248