3 papers
math.AP2026
Optimal regularity of stable harmonic maps to spheres
Xuanyu Li
In this paper, we show that the codimension of the singular set of a stable stationary harmonic map to a round -sphere is at least when is between 3 and 6, and is at l…
math.DG2026
Existence of constant mean curvature surfaces with controlled topology in 3-manifolds
Filippo Gaia, Xuanyu Li
We establish the existence of a non-trivial, branched immersion of a closed Riemann surface with constant mean curvature (CMC) into any closed, orientable 3-manifold $\math…
math.AP2026
Existence of expanding harmonic map flows to hemispheres
Xuanyu Li
We show the existence of non-trivial self-expanding harmonic map flows starting from non-energy-minimizing 0-homogeneous maps to a regular ball or a closed hemisphere. In particula…