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Two natural lower bounds are given by the sum of the endpoint displacements and by the angle between the initial and final directions of the segment. We characterize all pairs of segment positions for which either of these lower bounds is attained.
In arbitrary dimension, we obtain complete characterizations of the equality cases for both the endpoint-displacement bound and the angular bound.
From: Dragomir Grozev [view email]
[v1]
Mon, 22 Jun 2026 12:48:13 UTC (428 KB)
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