3 papers
math.DG2026
Area-minimizing capillary cones
Benjy Firester, Raphael Tsiamis, Yipeng Wang
We construct non-flat minimal capillary cones with bi-orthogonal symmetry groups for any dimension and contact angle. These cones interpolate between rescalings of a singular solut…
math.AP2026
Stability inequalities for one-phase cones
Benjy Firester, Raphael Tsiamis, Yipeng Wang
We obtain strict stability inequalities for homogeneous solutions of the one-phase Bernoulli problem. We prove that in dimension and above, cohomogeneity one solutions with bi-…
math.DG2025
On fill-ins with scalar curvature bounded from below and an inequality of Hijazi-Montiel-Roldán
Simon Brendle, Raphael Tsiamis, Yipeng Wang
We consider fill-ins of spin manifolds with scalar curvature bounded by . Gromov proposed a conjecture relating the infimum of the mean curvature of such a fill-in to the…