Plane curves and removable sets

On Removable Sets for Sobolev Spaces in the Plane

On Dense Sets Related To Plane Algebraic Curves

We show that certain subsets of Fq-rational points of the curve XZ n−1 = Y n are dense sets in P2(Fq).

Centre Symmetry Sets of Families of Plane Curves

We study centre symmetry sets and equidistants for a 1-parameter family of plane curves where, for a special member of the family, there exist two inflexions with parallel tangents. Some results can be obtained by reducing a generating family to normal forms, but others require direct calculation from the generating family. MSC2010 Classification: 57R45, 53A04, 53A15

On Partitions of Plane Sets into Simple Closed Curves

We investigate the conjecture that the complement in the euclidean plane E2 of a set F of cardinality less than the continuum c can be partitioned into simple closed curves iff F has a single point. The case in which F is finite was settled in [1] where it was used to prove that, among the compact connected two-manifolds, only the torus and the Klein bottle can be so partitioned. Here we prove ...

Removable Sets for Subharmonic Functions

It is a classical result that a closed exceptional polar set is removable for subharmonic functions which are bounded above. Gardiner has shown that in the case of a compact exceptional set the above boundedness condition can be relaxed by imposing certain smoothness and Hausdorff measure conditions on the set. We give related results for a closed exceptional set, by replacing the smoothness an...