For complete curves under the elastic flow, planar embeddedness is preserved below an optimal energy threshold near 10.906581, graphicality in any codimension below 8 − 4√2, and every self-intersecting complete planar curve has energy at least 8.
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Embeddedness and graphicality of the elastic flow for complete curves
For complete curves under the elastic flow, planar embeddedness is preserved below an optimal energy threshold near 10.906581, graphicality in any codimension below 8 − 4√2, and every self-intersecting complete planar curve has energy at least 8.