The article deals with several questions in harmonic analysis relating to curves in Euclidean space. These questions are well understood for non- degenerate curves, but poorly understood when the curve has degeneracies. The author points out that it is the affine arclength measure that is most relevant in this context. The questions discussed are:
1) For certain degenerate curves in , the construction of an analytic family of distributions adapted to the curve and containing the affine arclength measure.
2) Convolution estimates for the affine arclength measure on these curves.
3) Convolution estimates for the affine arclength measure on certain degenerate curves in
4) Restriction estimates for these curves.