Math Art
Lubeck-Batista Surface (doubly periodic Scherk-Costa)

Lubeck-Batista Surface (doubly periodic Scherk-Costa)

Lubeck-Batista Surface (doubly periodic Scherk-Costa) is a doubly periodic minimal surface, given by a Weierstrass representation, immersed, with a layer group.

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def-weierstrass doubly-periodic immersed implemented minimal minimal-periodic tradition-classical

Properties

Family
minimal-periodic
Given by
a Weierstrass representation
Curvature
zero mean curvature
Periodicity
doubly periodic
Ends
0
Embedding
immersed
Symmetry kind
layer group
Fidelity
exact
Exactness
numerical-integral

Definition

Doubly periodic 1-parameter family (2011) with genus 3 and four annular ends in the quotient: layers joined by Costa saddles keeping the Costa surface's straight lines, limiting in the Callahan-Hoffman-Meeks surface -- a doubly periodic version of it. THE SHIPPED ROW carries the notebook's seven solved (tau, a, b) members (tau = 0.935i .. 2.5i; default tau = i, (a, b) = (-0.16537041, 0.44637591)). The gate re-derives THE AUTHORS' OWN period conditions (paper Section 6, condition (9)) along the notebook's waypoint paths -- branch-tracked theta logs with a u^2 substitution at the (z - ib)^{-1/2} endpoint, where uniform quadrature leaves a ~3e-2 phantom residual that looks exactly like a wrong member -- and they vanish at every stored member (7e-6..3e-5). Deck structure gated: z -> z+1 = (0,0,1) EXACTLY, z -> z+tau purely horizontal; the seam branch is the measured reciprocal.

Sources

Derived from the Math Art generator registries and cross-referenced to the literature; not transcribed from any gallery's compilation.