Steven Finch

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math.DG2026

Schwarz $P$ and Schwarz $D$ as free-boundary minimal disks in a tetragonal disphenoid: exact areas

Steven Finch

Let $T$ be the tetragonal disphenoid whose four congruent faces are isosceles triangles with sides $2, 3, 3$ , so that the dihedral angles are $π /2$ along one opposite pair…

math.DG2026

An exact hypergeometric Weierstrass representation for Smyth's free-boundary minimal disk in the regular tetrahedron

Steven Finch

Smyth (1984) proved that every tetrahedron $T \subset R^{3}$ contains three embedded minimal disks meeting $\partial T$ orthogonally, obtained as conjugate surfaces of Plateau…

math.DG2026

Elimination of the parameters in an elliptic parametrization of the Schwarz primitive surface

Steven Finch

Let $Ω$ be the curvilinear square bounded by the four circular arcs $∣ ζ \mp 1∣ = 2$ , $∣ ζ \mp i ∣ = 2$ , and let $W = 1 + 14 ζ^{4} + ζ^{8}$ . Put \[ θ(ζ)=\arcsin\frac{2(1+i)ζ} {…

math.DG2026

The two cubic separable minimal surfaces: $D_{1} D_{2} D_{3} = 1$ and $C_{1} + C_{2} + C_{3} = 3 C_{1} C_{2} C_{3}$

Steven Finch

A minimal surface in $R^{3}$ is $separable$ if it is the zero set of $f (x) + g (y) + h (z)$ , and $isotropic$ if moreover $f = g = h$ . We announce that there are exac…

Schwarz P and Schwarz D as free-boundary minimal disks in a tetragonal disphenoid: exact areas

An exact hypergeometric Weierstrass representation for Smyth's free-boundary minimal disk in the regular tetrahedron

Elimination of the parameters in an elliptic parametrization of the Schwarz primitive surface

The two cubic separable minimal surfaces: D1​D2​D3​=1 and C1​+C2​+C3​=3C1​C2​C3​

Schwarz $P$ and Schwarz $D$ as free-boundary minimal disks in a tetragonal disphenoid: exact areas

The two cubic separable minimal surfaces: $D_{1} D_{2} D_{3} = 1$ and $C_{1} + C_{2} + C_{3} = 3 C_{1} C_{2} C_{3}$