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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.

##### MSC:
 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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