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Bol loop actions

Larissa V. Sbitneva (2000)

Commentationes Mathematicae Universitatis Carolinae

The notions of left Bol and Bol-Bruck actions are introduced. A purely algebraic analogue of a Nono family (Lie triple family), the so called Sabinin-Nono family, is given. It is shown that any Sabinin-Nono family is a left Bol-Bruck action. Finally it is proved that any local Nono family is a local left Bol-Bruck action. On general matters see [L.V. Sabinin 91, 99].

Boundaries of prescribed mean curvature

Eduardo H. A. Gonzales, Umberto Massari, Italo Tamanini (1993)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

The existence of a singular curve in R 2 is proven, whose curvature can be extended to an L 2 function. The curve is the boundary of a two dimensional set, minimizing the length plus the integral over the set of the extension of the curvature. The existence of such a curve was conjectured by E. De Giorgi, during a conference held in Trento in July 1992.

Bubbling on boundary submanifolds for the Lin–Ni–Takagi problem at higher critical exponents

Manuel del Pino, Fethi Mahmudi, Monica Musso (2014)

Journal of the European Mathematical Society

Let Ω be a bounded domain in n with smooth boundary Ω . We consider the equation d 2 Δ u - u + u n - k + 2 n - k - 2 = 0 in Ω , under zero Neumann boundary conditions, where Ω is open, smooth and bounded and d is a small positive parameter. We assume that there is a k -dimensional closed, embedded minimal submanifold K of Ω , which is non-degenerate, and certain weighted average of sectional curvatures of Ω is positive along K . Then we prove the existence of a sequence d = d j 0 and a positive solution u d such that d 2 | u d | 2 S δ K as d 0 in the sense of measures, where δ K ...

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