Related papers: Lagrangian surfaces with Legendrian boundary

Let $(M,g)$ be a closed Riemannian manifold and $L:TM\rightarrow \mathbb R$ be a Tonelli Lagrangian. In this thesis we study the existence of orbits of the Euler-Lagrange flow associated with $L$ satisfying suitable boundary conditions. We…

In this paper, we consider different versions of the classical Hopf's boundary lemma in the setting of the fractional $p-$Laplacian for $p \geq 2$. We start by providing for a new proof to a Hopf's lemma based on comparison principles.…

In this note we propose a min-max theory for embedded hypersurfaces with a fixed boundary and apply it to prove several theorems about the existence of embedded minimal hypersurfaces with a given boundary. A simpler variant of these…

We define the notion of an exceptional manifold to be a flat Riemannian manifold with boundary which supports a positive harmonic function satisfying simultaneously a zero Dirichlet condition and a constant (nonzero) Neumann condtion at the…

We consider a free boundary problem for the $p$-Laplace operator which is related to the so-called Bernoulli free boundary problem. In this formulation, the classical boundary gradient condition is replaced by a condition on the distance…

We examine the $L^2$-topology of the gauge orbits over a closed Riemann surface. We prove a subtle local slice theorem based on the div-curl Lemma of harmonic analysis, and deduce local pathwise connectedness and local uniform…

We consider nonhomogeneous fractional $p$-Laplace equations defined on a bounded nonsmooth domain which goes beyond the Lipschitz category. Under a sufficient flatness assumption on the domain in the sense of Reifenberg, we establish…

Some ideas and remarks are presented concerning a possible Lagrangian approach to the study of internal boundary conditions relating integrable fields at the junction of two domains. The main example given in the article concerns single…

In the framework of Special Bohr - Sommerfeld geometry it was established that an ample divisor in compact algebraic variety can define almost canonically certain real submanifold which is lagrangian with respect to the corresponding Kahler…

We recently established a Toponogov type triangle comparison theorem for a certain class of Finsler manifolds whose radial flag curvatures are bounded below by that of a von Mangoldt surface of revolution (arXiv:1205.3913). In this article,…

This paper presents necessary and sufficient optimality conditions for problems of the fractional calculus of variations with a Lagrangian depending on the free end-points. The fractional derivatives are defined in the sense of Caputo.

We prove necessary optimality conditions for problems of the calculus of variations on time scales with a Lagrangian depending on the free end-point.

In this paper we prove a desingularization theorem for Legendrian surfaces that are the conormal of a quasi-ordinary hypersurface.

In dimensions congruent to 1 modulo 4, we prove that the cotangent bundle of an exotic sphere which does not bound a parallelisable manifold is not symplectomorphic to the cotangent bundle of the standard sphere. More precisely, we prove…

We provide in this note two relevant examples of Lagrangian cobordisms. The first one gives an example of two exact Lagrangian submanifolds which cannot be composed in an exact fashion. The second one is an example of an exact Lagrangian…

Is it possible to obtain unbounded minimal surfaces in certain asymptotically flat 3-manifolds as a limit of solutions to a natural mountain pass problem with diverging boundaries? In this work, we give evidence that this might be true by…

We propose the graph description of Teichm\"uller theory of surfaces with marked points on boundary components (bordered surfaces). Introducing new parameters, we formulate this theory in terms of hyperbolic geometry. We can then describe…

We study Legendrian surfaces determined by cubic planar graphs. Graphs with distinct chromatic polynomials determine surfaces that are not Legendrian isotopic, thus giving many examples of non-isotopic Legendrian surfaces with the same…

In this paper, we study the Seiberg-Witten equations on the product R x Y, where Y is a compact 3-manifold with boundary. Following the approach of Salamon and Wehrheim in the instanton case, we impose Lagrangian boundary conditions for the…

This article studies the deformation problem for compact special Lagrangians with boundary in a Calabi--Yau manifold, with each boundary component constrained along a given Lagrangian submanifold. The tangent vectors generating such…