On the Ricci curvature of 3-submanifolds in the unit sphere
Sign Up to like & getrecommendations! Published in 2020 at "Archiv der Mathematik"
DOI: 10.1007/s00013-020-01515-7
Abstract: In this short note, studying 3-dimensional compact and minimal submanifolds of the $$(3+p)$$ ( 3 + p ) -dimensional unit sphere $${\mathbb {S}}^{3+p}(1)$$ S 3 + p ( 1 ) , we establish two rigidity… read more here.
Keywords: unit sphere; curvature submanifolds; submanifolds unit; ricci curvature ... See more keywords
An Explicit Isometric Reduction of the Unit Sphere into an Arbitrarily Small Ball
Sign Up to like & getrecommendations! Published in 2018 at "Foundations of Computational Mathematics"
DOI: 10.1007/s10208-017-9360-1
Abstract: Spheres are known to be rigid geometric objects: they cannot be deformed isometrically, i.e., while preserving the length of curves, in a twice differentiable way. An unexpected result by Nash (Ann Math 60:383–396, 1954) and… read more here.
Keywords: isometric reduction; unit; arbitrarily small; reduction unit ... See more keywords
Asymptotic behavior of gradient flows on the unit sphere with various potentials
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Differential Equations"
DOI: 10.1016/j.jde.2020.07.016
Abstract: Abstract We consider a multi-agent system whose dynamics is governed by a gradient flow on the unit sphere associated with the interaction potential between positions of all agents measured by a weighted distance | x… read more here.
Keywords: complete aggregation; asymptotic behavior; unit sphere; range ... See more keywords
The Mazur–Ulam property for two-dimensional somewhere-flat spaces
Sign Up to like & getrecommendations! Published in 2019 at "Linear Algebra and its Applications"
DOI: 10.1016/j.laa.2018.09.024
Abstract: Abstract In this paper, we show that if X is a two-dimensional real normed space such that its unit sphere contains a line segment with the distance between its endpoints being greater than 1, then… read more here.
Keywords: mazur ulam; property two; ulam property; unit sphere ... See more keywords
VANISHING THEOREMS FOR HYPERSURFACES IN THE UNIT SPHERE
Sign Up to like & getrecommendations! Published in 2018 at "Glasgow Mathematical Journal"
DOI: 10.1017/s0017089517000350
Abstract: Abstract Let Mn, n ≥ 3, be a complete hypersurface in $\mathbb{S}$n+1. When Mn is compact, we show that Mn is a homology sphere if the squared norm of its traceless second fundamental form is… read more here.
Keywords: harmonic forms; vanishing theorems; hypersurfaces unit; theorems hypersurfaces ... See more keywords
On the unit sphere of positive operators
Sign Up to like & getrecommendations! Published in 2019 at "Banach Journal of Mathematical Analysis"
DOI: 10.1215/17358787-2018-0017
Abstract: Given a C$^*$-algebra $A$, let $S(A^+)$ denote the set of those positive elements in the unit sphere of $A$. Let $H_1$, $H_2,$ $H_3$ and $H_4$ be complex Hilbert spaces, where $H_3$ and $H_4$ are infinite-dimensional… read more here.
Keywords: positive operators; unit sphere; sphere positive; unit ... See more keywords