7 problems

Let $u:\Sigma\times[0,T)\to N$ be a solution of harmonic map flow in the critical dimension $\dim(\Sigma)=2$, and define its body map by … Assume that the target $N$ is real-analyt…

Let $u_0:\mathbb{R}^n\rightarrow S^m$ be the initial map for a smooth expanding harmonic map flow, and suppose that its image is not contained in any $m$-dimensional linear subspac…

Topping's removable-discontinuity conjecture. The body map $u(T)$ will have only removable discontinuities.

Let $3\leq d\leq 6$, and let $\phi_1$ denote the globally regular shrinker solving … with exactly one intersection with $\frac{\pi}{2}$. Biernat–Bizoń conjecture. The shrinker…

Let … be the functional for the equivariant harmonic map problem, and let $f_e=\pi/2$ be the equator map. The Morse index of $f_e$ is the number of negative eigenvalues of the Hess…

Let $n\geq 2$, and consider the uniqueness theorem for weak solutions of the heat flow of harmonic maps into a compact Riemannian manifold $N$: if two solutions have gradients in…

Let $(M,g(t),\phi(t))$ be a solution of the Ricci–harmonic map flow $(RH)_\alpha$ on a maximal time interval $[0,T)$, and let $\operatorname{Rm}$ denote the Riemann curvature tenso…