We describe maximal nilpotent subsemigroups of a given nilpotency class in the semigroup Ωn of all n × n real matrices with nonnegative coefficients and the semigroup Dn of all doubly stochastic real matrices.

Let M and N be doubly connected Riemann surfaces with $${\mathscr {C}}^{1,\alpha }$$ boundaries nonvanishing conformal metrics $$\sigma $$ $$\wp respectively, assume that is a smooth metric bounded Gauss curvature $${\mathcal {K}}$$ finite area. Assume {H}}^\wp (M, N)$$ the class of all {W}}^{1,2}$$ homeomorphisms between {E}}^\wp : {\mathcal N)\rightarrow {\mathbf {R}}$$ Dirichlet-energy funct...

We prove that a Ricci curvature based method of triangulation of compact Riemannian manifolds, due to Grove and Petersen, extends to the context of weighted Riemannian manifolds and more general metric measure spaces. In both cases the role of the lower bound on Ricci curvature is replaced by the curvature-dimension condition CD(K,N). We show also that for weighted Riemannian manifolds the tria...

dually flat finsler metrics form a special and valuable class of finsler metrics in finsler information geometry,which play a very important role in studying flat finsler information structure. in this paper, we prove that everylocally dually flat generalized randers metric with isotropic s-curvature is locally minkowskian.

In [5] we showed, that a doubly transitive, non-solvable dimensional dual hyperoval D is either isomorphic to the Mathieu dual hyperoval or to a quotient of a Huybrechts dual hyperoval. In order to determine the doubly transitive dimensional dual hyperovals, it remains to classify the doubly transitive, solvable dimensional dual hyperovals and this paper is a contribution to this problem. A dou...

In this paper, by modifying Cheng-Yau$'$s technique to complete hypersurfaces in $S^{n+1}(1)$, we prove a rigidity theorem under the hypothesis of the mean curvature and the normalized scalar curvature being linearly related which improve the result of [H. Li, Hypersurfaces with constant scalar curvature in space forms, {em Math. Ann.} {305} (1996), 665--672].  

We establish some relative volume comparison theorems for extremal volume forms of‎ ‎Finsler manifolds under suitable curvature bounds‎. ‎As their applications‎, ‎we obtain some results on curvature and topology of Finsler manifolds‎. ‎Our results remove the usual assumption on S-curvature that is needed in the literature‎.

Let T be an arbitrary n × n matrix with real entries. We explicitly find the closest (in Frobenius norm) matrix A to T , where A is n × n with real entries, subject to the condition that A is “generalized doubly stochastic” (i.e. Ae = e and eA = e , where e = (1, 1, ..., 1) , although A is not necessarily nonnegative) and A has the same first moment as T (i.e. eT1 Ae1 = e T 1 Te1). We also expl...