All Questions

Let $0<a<d/2$, let $B$ be the unit ball in $\mathbb{R}^{d}$ centered at the origin, and let $f:B \to [0,\infty[$ be a a smooth function such that (1) $f(x)\geq f(0).$ (2) $\nabla f(x)\neq 0,\...

Consider a twice differentiable 1-strongly convex function $f:\mathbb{R}^n \to \mathbb{R}$. Is it true that there exists $\alpha>0$ independent of $n$ such that, for all $x \in \mathbb{R}^n$: \...

I am looking for a function $f:\mathbb C^2 \rightarrow \mathbb C^2$ that satisfies the two equations $$\partial_{z_2}f_1(z_1,z_2) + \partial_{z_1} f_2(z_1,z_2)=0 \text{ and }$$ $$\partial_{\bar z_1}...