Примитивные системы элементов в многообразиях ${\mathbf {A}}_m{\mathbf {A}}_n$: критерий и индуцирование.

Ч.К. Гупта; Е.И. Тимошенко

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The category of compactifications and its coreflections

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We define “the category of compactifications”, which is denoted , and consider its family of coreflections, denoted . We show that is a complete lattice with bottom the identity and top an interpretation of the Čech–Stone $β$ . A $c \in$ implies the assignment to each locally compact, noncompact $Y$ a compactification minimum for membership in the “object-range” of $c$ . We describe the minimum proper compactifications of locally compact, noncompact spaces, show that these generate...

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New stability results for spheres and Wulff shapes

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We prove that a closed convex hypersurface of the Euclidean space with almost constant anisotropic first and second mean curvatures in the $L^{p}$ -sense is $W^{2, p}$ -close (up to rescaling and translations) to the Wulff shape. We also obtain characterizations of geodesic hyperspheres of space forms improving those of [] and [].