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$\newcommand{\bR}{\mathbb{R}}\newcommand{\pa}{\partial}$This questions has some nebulous roots in Morse theory. The most general version goes as follows. Fix an integer $n\geq 2$. Suppose that we have ...

Let $M$ be a compact Riemannian manifold with boundary. How can one recognize whether the manifold can be foliated by strictly convex hypersurfaces? An exact definition is given below. If the ...