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Is a complete Riemannian manifold with positively pinched Ricci curvature compact
Lei Ni
https://arxiv.org/abs/2510.10279 https://arxiv.org/pdf/2510.10279

Is a complete Riemannian manifold with positively pinched Ricci curvature compact
A result of R. Hamilton asserts that any convex hypersurface in an Euclidian space with pinched second fundamental form must be compact. Partly inspired by this result, twenty years ago, in \cite{Ancient}, Remark 3.1 on page 650, the author formulated a problem asking if a complete Riemannian manifold with positively pinched Ricci curvature must be compact. There are several recent progresses, which are all rigidity results concerning the flat metric except the special case for the steady solit…

Universal Solution to Kronecker Product Decomposition
Daizhan Cheng
https://arxiv.org/abs/2509.22373 https://arxiv.org/pdf/2509.22373

Universal Solution to Kronecker Product Decomposition
This paper provides a general solution for the Kronecker product decomposition (KPD) of vectors, matrices, and hypermatrices. First, an algorithm, namely, monic decomposition algorithm (MDA), is reviewed. It consists of a set of projections from a higher dimension Euclidian space to its factor-dimension subspaces. It is then proved that the KPD of vectors is solvable, if and only if, the project mappings provide the required decomposed vectors. Hence it provides an easily verifiable necessary a…