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A manifold is a topological space that locally resembles Euclidean space near each point. More precisely, each point of an n-dimensional manifold has a neighbourhood that is homeomorphic to the Euclidean space of dimension n.
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Manifolds with a lower degree of regularity
Then, I would like to ask if does anyone know a reference where the theory for manifolds of class $W^2 L^{n-1,1}$, $C^{1,1}$ or $W^{m,p}$ (ordinary Sobolev Space) is discussed in detail. … In fact, I want to know, at least, how can be defined the mean curvature for these classes of manifolds. …