4 problems

Let $Y$ be a $CAT(0)$ space, let $u_0:\mathbb R^n\to Y$ satisfy $E(u_0)<\infty$ and $d(u_0,Q)\in L^\infty(\mathbb R^n)$ for some $Q\in Y$, and let $u$ be the suitable weak solution…

Let $\phi_1$ denote the first member of the infinite sequence of globally regular shrinker solutions of … Here the index $1$ denotes that $\phi_1$ has one intersection with…

Biernat's spectral stability conjecture. The associated linear operator has no unstable eigenvalues other than the gauge eigenvalue

Let $R(t)$ denote the blow-up scale for a generic $1$-corotational map, and let $T$ be its finite blow-up time. Generic blow-up rate conjecture. The generic blow-up is of Type II,…