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Exact Hessian Cancellation and Quartic Nondegeneracy at the Round Circle
Aya Ishizeki
We study the decomposed Möbius energies and at the round circle and determine their complete normal Hessians: and $H_2(C)=-(4π/3)(|D_s|^3-…
Upper and lower bounds and modulus of continuity of decomposed Möbius energies
Aya Ishizeki, Takeyuki Nagasawa
The Möbius energy is one of the knot energies, and is named after its Möbius invariant property. It is known to have several different expressions. One is in terms of the cosine of…
A Möbius invariant discretization and decomposition of the Möbius energy
Simon Blatt, Aya Ishizeki, Takeyuki Nagasawa
The Möbius energy, defined by O'Hara, is one of the knot energies, and named after the Möbius invariant property which was shown by Freedman-He-Wang. The energy can be decomposed i…
Decomposition of generalized O'Hara's energies
Aya Ishizeki, Takeyuki Nagasawa
O'Hara introduced several functionals as knot energies. One of them is the Möbius energy. We know its Möbius invariance from Doyle-Schramm's cosine formula. It is also known that t…