Manuscript En03-A@1 · En03-A.tex · section · 5398614e

Equal name data, unequal marked-slice data

External conical geometry and certified local moves › Equal name data, unequal marked-slice data · lines 1362–1387

En03-A@1#eq:fan

Choose $k \geq 3$ and

ϑ = \frac{2 π - μ}{k} < π, u_{j} = (cos ((j + \frac{1}{2}) ϑ), sin ((j + \frac{1}{2}) ϑ)) .

On sector $[j ϑ, (j + 1) ϑ]$ , let $β = tanh ζ$ and set

T = β u_{j} \cdot x .

The future unit normal is

n_{j} = cosh ζ e_{0} + sinh ζ (0, u_{j}) .

On a shared ray, both functions have value $β r cos (ϑ /2)$ ; the wedge faces match similarly. The result is a continuous piecewise-flat spacelike neighbourhood. Joining equal-radius ray endpoints by straight chords gives a finite polygonal star.

Displayed formulas in this passage

En03-A@1#eq:fan · line 1373
$T = β u_{j} \cdot x .$
unlabeled · line 1365
$ϑ = \frac{2 π - μ}{k} < π, u_{j} = (cos ((j + \frac{1}{2}) ϑ), sin ((j + \frac{1}{2}) ϑ)) .$
unlabeled · line 1378
$n_{j} = cosh ζ e_{0} + sinh ζ (0, u_{j}) .$

Equal name data, unequal marked-slice data

Displayed formulas in this passage

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