A global Morse index theorem and applications to Jacobi fields on CMC surfaces (Q6608790)

The author gives a global Morse index theorem for a \(CMC\) hypersurface \(M^n\) immersed in \(\mathbb{R}^{n+1}\) (Theorem A, formula (2.17)). \N\NThe paper is organized into six sections as follows : Introduction, Preliminary, Sobolev variation and a global Morse index theorem (the Sobolev setting, the spectral theorem, a global Morse index theorem), Sobolev continuity (examples, three-closure theorem, global version), Proof of Sobolev continuity, Distribution of Jacobi fields (unstable cones, distribution theorem). \N\NAnother paper by the author with \textit{C.-C. Lin} directly connected to this topic is [\textit{W.-H. Huang} and \textit{C.-C. Lin}, Arch. Ration. Mech. Anal. 141, No. 2, 105--116 (1998; Zbl 0941.53011)].