J. Spruck

activity

20072025

most citedThe half-space property and entire positive minimal graphs in M x R

30 citations · 81 across the 22 of their papers we have counts for

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18 papers · 1 filter

math.DG2025

Closed minimal hypersurfaces in $S^{5}$ with constant $S$ and $A_{3}$

Joel Spruck, Ling Xiao

In this paper, we prove that a closed minimally immersed hypersurface $M^{4} \subset S^{5}$ with constant $S := i = 1 \sum 4 λ_{i}^{2}$ and $A_{3} := i = 1 \sum 4 λ_{i}^{3}$ whose…

math.DG2023

An improved eigenvalue estimate for embedded minimal hypersurfaces in the sphere

Jonah A. J. Duncan, Yannick Sire, Joel Spruck

Suppose that $Σ^{n} \subset S^{n + 1}$ is a closed embedded minimal hypersurface. We prove that the first non-zero eigenvalue $λ_{1}$ of the induced Laplace-Beltrami operator on $…

math.DG2022

Rigidity of nonpositively curved manifolds with convex boundary

Mohammad Ghomi, Joel Spruck

We show that a compact Riemannian $3$ -manifold $M$ with strictly convex simply connected boundary and sectional curvature $K \leq a \leq 0$ is isometric to a convex domain in a compl…

math.DG2022

Minkowski inequality in Cartan-Hadamard manifolds

Mohammad Ghomi, Joel Spruck

Using harmonic mean curvature flow, we establish a sharp Minkowski type lower bound for total mean curvature of convex surfaces with a given area in Cartan-Hadamard 3-manifolds. Th…

math.DG2022

Total mean curvatures of Riemannian hypersurfaces

Mohammad Ghomi, Joel Spruck

We obtain a comparison formula for integrals of mean curvatures of Riemannian hypersurfaces, via Reilly's identities. As applications we derive several geometric inequalities for a…

math.DG2019

Convexity of constant mean curvature graphs in $R^{n + 1}$ with planar boundary

Joel Spruck, Liming Sun

We study the Dirichlet problem for a graph $Σ$ in $R^{n + 1}$ with normalized constant mean curvature $H > 0$ and planar boundary $Γ = \partial Ω$ . Our main result is that the o…

Closed minimal hypersurfaces in S5 with constant S and A3​

An improved eigenvalue estimate for embedded minimal hypersurfaces in the sphere

Rigidity of nonpositively curved manifolds with convex boundary

Minkowski inequality in Cartan-Hadamard manifolds

Total mean curvatures of Riemannian hypersurfaces

Convexity of constant mean curvature graphs in Rn+1 with planar boundary

Closed minimal hypersurfaces in $S^{5}$ with constant $S$ and $A_{3}$

Convexity of constant mean curvature graphs in $R^{n + 1}$ with planar boundary