= Radial dilation tangency to homogeneous zero sets
{title2=$H(\lambda x)=\lambda^dH(x)\ \Longrightarrow\ x\cdot\nabla H=dH$}
Differentiate the displayed homogeneity relation in $\lambda$ at $1$. On every regular point of $H=0$, the radial <vector field> $x$ is therefore perpendicular to the normal <gradient> and tangent to the level surface. Its flow $x(t)=e^t x(0)$ preserves that zero set. At a singular vertex this flow formulation remains meaningful even if there is no tangent plane.
Back to article page
