A criterion for the harmonicity of the Grassmann map of an immersed smooth submanifold in some Lie group with left-invariant metric is given. Using the obtained expression, we obtain criteria for the harmonicity of this ...
We give upper and lower estimates for the ratio between the volume of a metric ball and the area of its surface in Finsler–Hadamard manifolds with pinched S-curvature. We apply these estimates to get the limit at infinity ...
We show that the spheres in the Hilbert geometry have the same volume growth rate as those in the Lobachevsky space. We give the asymptotic estimates for the ratio of the volume of a metric ball to the area of a metric ...