3 problems

Liu–Pego's local convexity conjecture. Every such map $\phi$ must necessarily be locally convex in $\Omega$.

Let $M$ be the centered Hardy--Littlewood maximal operator on $fR$, and let $f\in\operatorname{BV}(fR)$ have limits $f(\infty)$ and $f(-\infty)$ at the two ends. Write…

Nested-fractal variation conjectures.