4 problems

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Legendre-transform variable conjecture for dual action principles
Let $v$ be a primal field and let $p$ be the variable obtained from $v$ by a change of variables motivated by a Legendre transform. Consider the resulting dual action and the intro…
Conjectureopendislocation-dynamics legendre-transforms variational-principlesarXiv posted 2 days ago
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The prehomogeneous-space conjecture for homaloidal EKP-polynomials
Prehomogeneous-space conjecture. Any homaloidal EKP-polynomial is a relative invariant of a regular prehomogeneous space.
Conjectureopenhomaloidal-polynomials legendre-transforms prehomogeneous-spacesarXiv posted 2 days ago
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Conjecture C on $b$ -functions under iterated polarization and Legendre transform
Let $F$ be an $N$ -variable homaloidal polynomial of degree $r$ , and put $H=\mathcal{ML}(F)$ . Let $b^{[0]}(s)$ denote a $b$ -function for the pair $(F,H)$ . For each $k$ , let…
Conjecturesolvedb-functions homaloidal-polynomials legendre-transformsarXiv posted 2 days ago
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Conjecture B on $b$ -functions of polarized sub-Hankel determinants
Let $F_k^{(r)}$ be the $k$ -times polarization of the size- $r$ sub-Hankel determinant $P_1$ , and let $H_k$ be its multiplicative Legendre transform. Conjecture B. The corresponding…
Conjecturesolvedb-functions legendre-transforms sub-hankel-determinantsarXiv posted 2 days ago

Legendre-transform variable conjecture for dual action principles