Raphael Tsiamis

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20232026

most citedEigenvalue estimates on shrinkers

1 citations · 1 across the 17 of their papers we have counts for

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math.DG2026

Ricci flow on manifolds with positive isotropic curvature in all dimensions

Simon Brendle, Raphael Tsiamis

We extend the classification of manifolds with positive isotropic curvature to all dimensions $n \geq 5$ . This result also completes the classification of uniformly positive isotro…

math.DG2026

The sharp isoperimetric inequality for varifolds in codimension two

Raphael Tsiamis

We prove a Michael-Simon inequality for a class of varifolds in Euclidean space that includes all integral varifolds with locally bounded first variation of arbitrary dimension and…

math.DG2026

The anisotropic Michael-Simon inequality

Benjy Firester, Raphael Tsiamis

We prove a Michael-Simon inequality for varifolds of every dimension and codimension with respect to anisotropic energies. In particular, this resolves the problem for every convex…

math.DG2026

The anisotropic Michael-Simon inequality for surfaces in every codimension

Benjy Firester, Raphael Tsiamis

We prove a Michael-Simon inequality for $2$ -varifolds in $R^{N}$ , in arbitrary codimension, for anisotropies sufficiently close to the area functional. Building on the ideas…

math.DG2026

Stable $s$ -minimal cones in $R^{3}$ are flat for $s$ close to zero

Raphael Tsiamis

We prove that stable nonlocal minimal cones in three dimensions are flat, for $s$ sufficiently close to zero. Our approach develops new structural properties of stable $s$ -minimal…

math.DG2026

On Chern's conjecture for minimal submanifolds of the sphere

Benjy Firester, Raphael Tsiamis

A well-known conjecture of Chern, do Carmo, and Kobayashi asserts that, for $n, m \geq 1$ , the scalar curvature of a closed, minimally immersed $n$ -submanifold of $S^{n + m}$ …

math.DG2026

Sharp systolic inequalities for Kähler manifolds

Raphael Tsiamis

We establish sharp inequalities for two-dimensional systolic invariants of metrics with positive scalar curvature: the $2$ -systole and the spherical $2$ -systole of compact Kähler m…

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…

math.DG2024

Classification of Semigraphical Translators

Francisco Martín, Mariel Sáez, Raphael Tsiamis +1

We complete the classification of semigraphical translators for mean curvature flow in $R^{3}$ that was initiated by Hoffman-Martín-White. Specifically, we show that there i…

math.DG2024

Cohomogeneity two Ricci solitons with sub-Euclidean volume

Benjy Firester, Raphael Tsiamis

We introduce new families of four-dimensional Ricci solitons of cohomogeneity two with volume collapsing ends. In a local presentation of the metric conformal to a product, we redu…

math.DG2024★ 1 cited

Eigenvalue estimates on shrinkers

S. Brendle, R. Tsiamis

We prove an eigenvalue estimate which holds on every properly embedded shrinker for mean curvature flow. This generalizes earlier work of Ding and Xin to the noncompact case.

math.DG2023

Uniqueness of Semigraphical Translators

Francisco Martín, Mariel Sáez, Raphael Tsiamis

We prove a conjecture by Hoffman, White, and the first author regarding the uniqueness of pitchfork and helicoid translators of the mean curvature flow in $R^{3}$ . We employ…

Ricci flow on manifolds with positive isotropic curvature in all dimensions

The sharp isoperimetric inequality for varifolds in codimension two

The anisotropic Michael-Simon inequality

The anisotropic Michael-Simon inequality for surfaces in every codimension

Stable s-minimal cones in R3 are flat for s close to zero

On Chern's conjecture for minimal submanifolds of the sphere

Sharp systolic inequalities for Kähler manifolds

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

Classification of Semigraphical Translators

Cohomogeneity two Ricci solitons with sub-Euclidean volume

Eigenvalue estimates on shrinkers

Uniqueness of Semigraphical Translators

Stable $s$ -minimal cones in $R^{3}$ are flat for $s$ close to zero

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