Sum of squares and the Łojasiewicz exponent at infinity
Sum of squares and the Łojasiewicz exponent at infinity
Let $V\subset \mathbf {\mathbb {R}}^n$, $n\ge 2$, be an unbounded algebraic set defined by a system of polynomial equations $h_1(x)=\cdots =h_r(x)=0$ and let $f:\mathbf {\mathbb {R}}^n\to \mathbf {\mathbb {R}}$ be a polynomial. It is known that if $f$ is