BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ian Fleschler (Princeton University) DTSTART:20250319T110000Z DTEND:20250319T130000Z DTSTAMP:20260423T041343Z UID:NCTS-GMT/28 DESCRIPTION:Title: A sharp extension of Allard’s boundary regularity theorem for area min imizing currents with arbitrary boundary multiplicity\nby Ian Fleschle r (Princeton University) as part of NCTS international Geometric Measure T heory seminar\n\n\nAbstract\nIn the context of area-minimizing currents\, Allard boundary regularity\ntheorem asserts that an oriented current with boundary that minimizes\narea cannot have boundary singularities of minimu m density. Indeed\, in a\nneighborhood of a point of minimum density\, the surface must coincide\nwith a classical smooth minimal surface that attac hes smoothly to the\nboundary.\n\nIn this talk\, I will discuss a series o f papers\, one of them in\ncollaboration with Reinaldo Resende\, that exte nd Allard’s boundary\nregularity theory to a higher boundary multiplicit y setting.\nSpecifically\, for an area-minimizing current with a multiplic ity $Q$\nboundary\, we study density $Q/2$ boundary points. In this contex t\, a\nregular point is one where smooth submanifolds with multiplicity at tach\ntransversally to the boundary. We establish that the set of singular \nboundary points of minimum density is of boundary codimension at most 2\ nand rectifiable\, extending the corresponding result in 2d by De Lellis - \nSteinbrüchel - Nardulli to higher dimensional currents. The sharpness o f\nthis regularity theory is confirmed by my construction of a\n3-dimensio nal area mininimizing current in $\\mathbb R^5$ with a singular\nboundary point of minimum density.\n LOCATION:https://researchseminars.org/talk/NCTS-GMT/28/ END:VEVENT END:VCALENDAR