2010/10/09 by Harold Rosenberg, Graham Smith, Rosenberg, Harold +1 · 1 citation
Mathematics · #58B05 #58C40 #58D10 #58J05 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.1010.1879
openalex publication_date 2010/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 M.