Let $\gamma_1,\gamma_2:[0,1]\to \mathbb{R}^2$ - smooth curve, $\gamma_i(0)=\gamma_i(1)$, $X_1$ and $X_2$ are the areas bounded by the corresponding curves. . Suppose we have an $X_1 $-shaped hole, and into this hole we want to push as large an area of a rigid $X_2$-shape form. How to calculate the largest such area for two given $\gamma_1$ and $\gamma_2$? More precisely, to what problem with a known solution can I reduce this problem?
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$\begingroup$ I don’t think this has a general solution $\endgroup$– user44143Commented Sep 30, 2021 at 2:59
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$\begingroup$ Oh, this is expected. Therefore, I would like to see some work on topics related to this task. $\endgroup$– Ben TomCommented Sep 30, 2021 at 12:18
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1$\begingroup$ “What is work related to this?” is not a good question for this site, but you can browse relevant tags (like convex-geometry) and questions (like mathoverflow.net/questions/342037/…) $\endgroup$– user44143Commented Sep 30, 2021 at 12:48
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