Raphael Tsiamis

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math.DG2026

Mean curvature flows with prescribed singular sets

Raphael Tsiamis

For every closed set $K \subset R^{n}$ and every $m \geq 2$ , we construct a mean-convex ancient solution to mean curvature flow of hypersurfaces in $R^{m + n}$ , with…

math.DG2026

Topology of minimal surfaces in the sphere from capillarity

Benjy Firester, Raphael Tsiamis

We present a general construction of embedded minimal and constant mean curvature surfaces in $S^{n}$ and one-phase free boundaries joined by a smooth interpolation by capil…

math.DG2026

New minimal surfaces in the sphere from capillary minimal cones

Benjy Firester, Raphael Tsiamis

For every $p, q \geq 1$ , we construct minimal embeddings of $S^{p} \times S^{q} \times S^{1}$ in $S^{p + q + 2}$ by doubling the links of free-boundary…

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.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 $- n (n - 1)$ . Gromov proposed a conjecture relating the infimum of the mean curvature of such a fill-in to the…

math.DG2025

Uniqueness of Cylindrical Tangent Cones $C_{p, q} \times R$

Benjy Firester, Raphael Tsiamis, Yipeng Wang

We show the uniqueness of the cylindrical tangent cone $C (S^{2} \times S^{4}) \times R$ for area-minimizing hypersurfaces in $R^{9}$ , completing the u…

Mean curvature flows with prescribed singular sets

Topology of minimal surfaces in the sphere from capillarity

New minimal surfaces in the sphere from capillary minimal cones

Area-minimizing capillary cones

On fill-ins with scalar curvature bounded from below and an inequality of Hijazi-Montiel-Roldán

Uniqueness of Cylindrical Tangent Cones Cp,q​×R

Uniqueness of Cylindrical Tangent Cones $C_{p, q} \times R$