Some geometric inequalities for varifolds on Riemannian manifolds based on monotonicity identities
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DOI: 10.1007/s10455-021-09822-0
Abstract: Using Rauch’s comparison theorem, we prove several monotonicity inequalities for Riemannian submanifolds. Our main result is a general Li–Yau inequality which is applicable in any Riemannian manifold whose sectional curvature is bounded above (possibly positive).… read more here.
Keywords: geometric inequalities; monotonicity; inequalities varifolds; riemannian manifolds ... See more keywords
Integral geometric inequalities and valuations
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DOI: 10.1007/s10711-019-00460-2
Abstract: General integral geometric invariants for convex bodies are introduced and two integral geometric inequalities for them are established. The equality cases for the inequalities are kinematic formulas, which are characterizations of integral geometric valuations. Those… read more here.
Keywords: geometric inequalities; inequalities valuations; integral geometric;
Norm estimates for k-plane transforms and geometric inequalities
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DOI: 10.1016/j.aim.2019.04.012
Abstract: The article is devoted to remarkable interrelation between the norm estimates for $k$-plane transforms in weighted and unweighted $L^p$ spaces and geometric integral inequalities for cross-sections of measurable sets in $\mathbb{R}^n$. We also consider more… read more here.
Keywords: transforms geometric; geometric inequalities; plane transforms; norm estimates ... See more keywords