0000000000394136
AUTHOR
A. Montesinos Amilibia
Dido's problem in the plane for domains with fixed diameter
We find the connected compact domains in the closed half-plane, with fixed area and diameter, which minimize the relative perimeter.
A knot without tritangent planes
We show, with computations aided by a computer, that the (3,2)-curve on some standard torus (which topologically is the trefoil knot) has no tritangent planes, thus answering in the negative a conjecture of M. H. Freedman.
Conformal curvatures of curves in
Abstract We define a complete set of conformal invariants for pairs of spheres in and obtain from these the expressions of the conformal curvatures of curves in (n + 1)-space in terms of the Euclidean invariants.
A Dido problem for domains in ?2 with a given inradius
We find which are the simply connected domains in ℝ2 satisfying the Dido condition for a straight shoreline, with a given area A and a fixed inradius ϱ, which minimize the length of the free boundary. There are three different cases according to the values of A and ϱ.
A knot without triple bitangency
It is proved that certain trefoil knot has not triple bitangency, answering thus in the negative a conjecture of S. Izumiya and W. L. Marar.