Extensions of k-regulous functions from two-dimensional varieties

2023/03/04 by Banecki, Juliusz
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2303.02481

Abstract

We prove that a k-regulous function defined on a two-dimensional non-singular affine variety can be extended to an ambient variety. Additionally we derive some results concerning sums of squares of k-regulous functions; in particular we show that every positive semi-definite regular function on a non-singular affine variety can be written as a sum of squares of locally Lipschitz regulous functions.

Related

• Extension of k-regulous functions from varieties of arbitrary dimension
• Seminormalization and regulous functions on complex affine varieties
• Maximal ideals in the ring of regulous functions are not finitely\n generated
• Integration of nonsmooth \boldsymbol2-forms: from Young to Itô and Stratonovich
• Second order conditions to decompose smooth functions as sums of squares