BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Manuel Ritoré (Universidad de Granada) DTSTART:20200529T150000Z DTEND:20200529T160000Z DTSTAMP:20260423T021529Z UID:ISRS/4 DESCRIPTION:Title: Wul ff shapes in the Heisenberg group\nby Manuel Ritoré (Universidad de G ranada) as part of International sub-Riemannian seminar\n\n\nAbstract\nGiv en a not necessarily symmetric left-invariant norm $||\\cdot ||_K$ in\nthe first Heisenberg group $\\mathbb{H}^1$ induced by a convex body\n$K\\subs et\\mathbb{R}^2$ containing the origin in its interior\, we\nconsider the associated perimeter functional\, that coincides with the\nclassical sub-R iemannian perimeter in case $K$ is the closed unit disk\ncentered at the o rigin of $\\rr^2$. Under the assumption that $K$ has\nstrictly convex smoo th boundary we compute the first variation formula\nof perimeter for sets with $C^2$ boundary. The localization of the\nvariational formula in the n on-singular part of the boundary\, composed\nof the points where the tange nt plane is not horizontal\, allows us to\ndefine a mean curvature functio n $H_K$ out of the singular set. In the\ncase of non-vanishing mean curvat ure\, the condition that $H_K$ be\nconstant implies that the non-singular portion of the boundary is\nfoliated by horizontal liftings of translation s of $\\ptl K$ dilated by a\nfactor of $1/H_K$. Based on this we can defin ed a sphere $\\mathbb{B}_K$\nwith constant mean curvature $1$ by consideri ng the union of all\nhorizontal liftings of $\\partial K$ starting from $( 0\,0\,0)$ until they\nmeet again. We give some geometric properties of thi s sphere and\,\nmoreover\, we prove that\, up to non-homogenoeus dilations and\nleft-translations\, they are the only solutions of the sub-Finsler\n isoperimetric problem in a restricted class of sets. This is joint work\nw ith Julián Pozuelo.\n LOCATION:https://researchseminars.org/talk/ISRS/4/ END:VEVENT END:VCALENDAR