We prove that every singular algebraic curve in ℝⁿ admits local tangential Markov inequalities at each of its points. More precisely, we show that the Markov exponent at a point of a real algebraic curve A is less than or equal to twice the multiplicity of the smallest complex algebraic curve containing A.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap86-1-7, author = {Laurent Gendre}, title = {Inegalites de Markov tangentielles locales sur les courbes algebriques singulieres de Rn}, journal = {Annales Polonici Mathematici}, volume = {85}, year = {2005}, pages = {59-77}, zbl = {1112.41009}, language = {fra}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap86-1-7} }
Laurent Gendre. Inégalités de Markov tangentielles locales sur les courbes algébriques singulières de ℝⁿ. Annales Polonici Mathematici, Tome 85 (2005) pp. 59-77. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap86-1-7/