Smooth submanifolds intersecting any analytic curve in a discrete set

We construct examples of $C^\infty$ smooth submanifolds in ${\Bbb C}^n$ and ${\Bbb R}^n$ of codimension 2 and 1, which intersect every complex, respectively real, analytic curve in a discrete set. The examples are realized either as compact tori or as properly imbedded Euclidean spaces, and are the graphs of quasianalytic functions. In the complex case, these submanifolds contain real $n$-dimensional tori or Euclidean spaces that are not pluripolar while the intersection with any complex analytic disk is polar

Quasianalyticity and pluripolarity

We show that the graph $$\Gamma_f=\{(z,f(z))\in{\Bbb C}^2: z\in S\}$$ in ${\Bbb C}^2$ of a function $f$ on the unit circle $S$ which is either continuous and quasianalytic in the sense of Bernstein or $C^\infty$ and quasianalytic in the sense of Denjoy is pluripolar

Bernstein-Markov: a survey

We give a survey of recent results, due mainly to the authors, concerning Bernstein-Markov type inequalities and connections with potential theory.Comment: This will appear soon in a special issue of Dolomites Research Notes on Approximation (DRNA): "Ten years of Padua Points

A Cantor set whose polynomial hull contains no analytic discs

A generalization of a result of Wermer concerning the existence of polynomial hulls without analytic discs is presented. As a consequence it is shown that there exists a Cantor set $X$ in ${\mathbb C}^3$ whose polynomial hull is strictly larger than $X$ but contains no analytic discs.Comment: The paper has been almost completely rewritten. A much shorter, but less direct, proof is given that yields a stronger resul