Conformal Mapping of Unbounded Multiply Connected Regions onto Canonical Slit Regions

<table>The original region <svg height="11.6125" id="M633" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 20.6 11.6125" width="20.6" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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l-26 29t-28 35.5l-23 37.5t-20.5 43t-12 45.5t-5.5 51q0 133 88 218.5t219 85.5q132 0 218 -83t86 -218q0 -40 -11.5 -78t-33 -71.5t-39 -56t-44 -51t-32.5 -35.5h84q35 0 48 12t31 63z" id="x3A9"></path></g>
<g transform="matrix(.012,0,0,-.012,12.925,3.4)"><path d="M535 230h-483v50h483v-50z" id="x2212"></path></g>
</svg> and its canonical images with <svg height="19.362499" id="M634" style="vertical-align:-5.73167pt" version="1.1" viewbox="0 0 60.900002 19.362499" width="60.900002" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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t63 -51q34 0 64 28.5t52.5 77t39 103t28.5 115.5z" id="x1D703"></path></g>
<g transform="matrix(.012,0,0,-.012,8.525,16.25)"><path d="M570 304q0 -108 -87 -199q-40 -42 -94.5 -74t-105.5 -43q-41 0 -65 11l-29 -141q-9 -45 -1.5 -58t45.5 -16l26 -2l-5 -29l-241 -10l4 26q51 10 67.5 24t26.5 60l113 520q-54 -20 -89 -41l-7 26q38 28 105 53l11 49q20 25 77 58l8 -7l-17 -77q39 14 102 14q82 0 119 -36
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<g transform="matrix(.017,0,0,-.017,20.925,12.163)"><path d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" id="x3D"></path></g><g transform="matrix(.017,0,0,-.017,35.612,12.163)"><path d="M574 449q-23 -58 -38 -79q-16 -4 -79 -4q-27 -100 -46 -219q-14 -87 7 -87t74 36l13 -27q-74 -81 -139 -81q-48 0 -48 62q0 22 8 59l60 258l-154 4q-21 -103 -54.5 -209t-64.5 -151q-38 -23 -83 -23l-7 15q46 36 94 152.5t64 216.5q-81 0 -138 -54l-18 23q22 27 39.5 43
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</svg> for parallel slits.          </table>

Abstract and Applied Analysis

fig3

Figure 3

Figure 3: Conformal Mapping of Unbounded Multiply Connected Regions onto Canonical Slit Regions 