Degree theory of immersed hypersurfaces - Rosenberg, H. (Harold), 1941-; Smith, Graham (Graham Andrew Craig) (Memoirs of the American Mathematical Society, 2020)
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 -χ(M), where χ(M) is the Euler characteristic of the ambient manifold M.