Calculus of Variations and Geometric Measure Theory

S. Delladio

Taylor's polynomials and non-homogeneous blow-ups

created on 07 Aug 2002


Submitted Paper

Inserted: 7 aug 2002

Year: 2002


The graph of a function $f$ is subjected to non-homogeneous dilatations around $(x_0;f(x_0))$, related to the Taylor's expansion of $f$ at $x_0$. Some natural questions about convergence are considered and answered. Finally, it is provided a counterexample to a statement which was presumed to be true (hence erroneously!) in J.H.G. Fu, Some Remarks On Legendrian Rectifiable Currents, Manuscripta Math. $97$, n. 2, 175-187 (1998).

Keywords: non-homogeneous blow-ups, Taylor polynomials, counterexamples