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Mean curvature comparison for tubular hypersurfaces in symmetric spaces. (English) Zbl 1063.53063
The authors obtain some comparison theorems for the mean curvature of tubular hypersurfaces \(P_t\) around a submanifold \(P\) in a Riemannian manifold \(M\), with bounded curvature. The problem has as model the theory of tubular hypersurfaces around totally geodesic, curvature preserving submanifolds in symmetric spaces of arbitrary rank. Moreover, they obtain a comparison result for the relative volume using as model totally geodesic submanifolds in a symmetric space for which the first conjugate locus and the cut-focal locus do coincide.

53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53C35 Differential geometry of symmetric spaces
53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions
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