1 - 10 of 12 articles
AbstractWe prove that there exist non-trivial (i.e. not Einstein) Ricci solitons on non-conformally flat four-dimensional Lorentzian Walker manifolds. Moreover, we show that only steady Ricci solitons may be gradient ones.
AbstractLet π be a subplane of PG(2,q3) of order q that is exterior to ℓ∞. The exterior splash of π is the set of q2+q+1 points on ℓ∞ that lie on the extended lines of π. Exterior splashes are projectively equivalent to scattered linear sets of rank 3, covers of the circle geometry CG(3,q), and...
AbstractLet M be a complete connected C2-surface in ℝ3 in general position, intersecting some plane along a clean figure-8 (a loop with total curvature zero) and such that all compact intersections with planes have central symmetry. We prove that M is a (geometric) cylinder over some central...
AbstractVieta’s classical formulae explicitly determine the coefficients of a polynomial p ∈ 𝔽[x] in terms of the roots of p, where 𝔽 is any commutative ring. In this paper, Vieta’s formulae are obtained for slice-regular polynomials over the noncommutative algebra of quaternions, by an argument...
AbstractWe prove that sausages are the family of ‘extremal sets’ in relation to certain linear improvements of Minkowski’s first inequality when working with projection/sections assumptions. In particular they characterize the equality cases of the corresponding linear refinements of both the...
AbstractNew types of maximal symplectic partial spreads are constructed.
AbstractWe study S-convex sets, which are the geometric objects obtained as the intersection of the usual convex sets in ℝd with a proper subset S ⊂ ℝd, and contribute new results about their S-Helly numbers. We extend prior work for S = ℝd, ℤd, and ℤd−k × ℝk, and give some sharp bounds for...
AbstractUsing the semidiameter (in connection to the mean radius and surface radius) of a convex closed hypersurface in ℝn, n ≥ 2, as a sharp upper bound of the variational p-capacity radius where p ∈ (1,n), this paper settles a restriction or variant of S.-T. Yau’s Problem 59 in  from the...
AbstractWe show that a 30° circular sector of unit radius contains an isometric copy of every drapeable unit arc, and we describe the family of drapeable exit arcs of unit length in the sector. The conjecture that this sector is a cover for the family of all unit arcs remains unresolved.
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