Variational formulae and estimates of O’Hara’s knot energies
| Autor: | Takeyuki Nagasawa, Shoya Kawakami |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Journal of Knot Theory and Its Ramifications. 29:2050017 |
| ISSN: | 1793-6527 0218-2165 |
| DOI: | 10.1142/s0218216520500170 |
| Popis: | O’Hara’s energies, introduced by Jun O’Hara, were proposed to answer the question what the canonical shape in a given knot type is, and were configured so that the less the energy value of a knot is, the “better” its shape is. The existence and regularity of minimizers has been well studied. In this paper, we calculate the first and second variational formulae of the [Formula: see text]-O’Hara energies and show absolute integrability, uniform boundedness, and continuity properties. Although several authors have already considered the variational formulae of the [Formula: see text]-O’Hara energies, their techniques do not seem to be applicable to the case [Formula: see text]. We obtain the variational formulae in a novel manner by extracting a certain function from the energy density. All of the [Formula: see text]-energies are made from this function, and by analyzing it, we obtain not only the variational formulae but also the estimates in several function spaces. |
| Databáze: | OpenAIRE |
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