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4 papers · 2 filters
Short Homotopically independent loops on surfaces
Steve Karam
In this paper, we are interested in short homologically and homotopically independent loops based at the same point on Riemannian surfaces and metric graphs. First, we show that fo…
On the Entropies of Hypersurfaces with bounded mean curvature
Said Ilias, Barbara Nelli, Marc Soret
We are interested in the impact of entropies on the geometry of a hypersurface of a Riemannian manifold. In fact, we will be able to compare the volume entropy of a hypersurface wi…
Complete minimal submanifolds of compact Lie groups
Sigmundur Gudmundsson, Martin Svensson, Marina Ville
We give a new method for manufacturing complete minimal submanifolds of compact Lie groups and their homogeneous quotient spaces. For this we make use of harmonic morphisms and bas…
Growth of balls in the universal cover of surfaces and graphs
Steve Karam
In this paper, we prove uniform lower bounds on the volume growth of balls in the universal covers of Riemannian surfaces and graphs. More precisely, there exists a constant …