arXiv subjects

Filippo Morabito

Publications and source records attributed to Filippo Morabito.

7 recordsLinked to original sources

arXiv2016

Towering phenomena for the Yamabe equation on symmetric manifolds

Let $(M,g)$ be a compact smooth connected Riemannian manifold (without boundary) of dimension $N\ge7$. Assume $M$ is symmetric with respect to a point $ξ_0$ with non-vanishing Weyl's tensor. We consider the linear perturbation of the Yamabe problem $$(P_ε)\qquad-\mathcal L_g u+εu=u^{N+2\over N-2}\ \hbox{in}\ (M,g) .$$ We prove that for any $k\in \mathbb N$, there exists $ε_k>0$ such that for all $ε\in (0, ε_k)$ the problem $(P_ε)$ has a symmetric solution $u_ε,$ which looks like the superposition of $k$ positive bubbles centered at the point $ξ_0$ as $ε\to 0$. In particular, $ξ_0$ is a {\em towering} blow-up point.

math.AP↗

arXiv2013

Delaunay type domains for an overdetermined elliptic problem in S^n x R and H^n x R

We prove the existence of a countable family of Delaunay type domains Ω_j in M^n x R, where M^n is the Riemannian manifold S^n or H^n and n is at least 2, bifurcating from the cylinder B^n x R (where B^n is a geodesic ball of radius 1 in M^n) for which the first eigenfunction of the Laplace-Beltrami operator with zero Dirichlet boundary condition also has constant Neumann data at the boundary. The domains Ω_j are rotationally symmetric and periodic with respect to the R-axis of the cylinder and as j converges to 0 the domain Ω_j converges to the cylinder B^n x R.

math.DG↗

arXiv2010

Non-periodic Riemann examples with handles

We show the existence of 1-parameter families of non-periodic, complete, embedded minimal surfaces in euclidean space with infinitely many parallel planar ends. In particular we are able to produce finite genus examples and quasi-periodic examples of infinite genus.

math.DG↗

arXiv2010

Classification of rotational special Weingarten surfaces of minimal type in S^2 x R and H^2 x R

In this paper we finish the classification of rotational special Weingarten surfaces in S^2 x R and H^2 x R; i.e. rotational surfaces in S^2 x R and H^2 x R whose mean curvature h and extrinsic curvature K_e satisfy h=f(h^2-K_e), for some function f in C^1([0,+infty)) such that 4x(f'(x))^2<1 for any x>=0.

math.DG↗

arXiv2009

Saddle towers in H^2 x R

Given k>=2, we construct a (2k-2)-parameter family of properly embedded minimal surfaces in H^2 x R invariant by a vertical translation T, called Saddle Towers, which have total intrinsic curvature 4 pi(1-k), genus zero and 2k vertical Scherk-type ends in the quotient by T. As limits of those Saddle Towers, we obtain Jenkins-Serrin graphs over ideal polygonal domains (with total intrinsic curvature 2 pi(1-k)); we also get properly embedded minimal surfaces which are symmetric with respect to a horizontal slice and have total intrinsic curvature 4 pi(1-k), genus zero and k vertical planar ends.

math.DG↗

arXiv2008

An end-to-end-construction for singly periodic minimal surfaces

We show the existence of various families of properly embedded singly periodic minimal surfaces in R^3 with finite arbitrary genus and Scherk type ends in the quotient. The proof of our results is based on the gluing of small perturbations of pieces of already known minimal surfaces.

math.DG↗

arXiv2008

Index and nullity of the Gauss map of the Costa-Hoffman-Meeks surfaces

The aim of this work is to extend the results of S. Nayatani about the index and the nullity of the Gauss map of the Costa-Hoffman-Meeks surfaces for values of the genus bigger than 37. That allows us to state that these minimal surfaces are non degenerate for all the values of the genus in the sense of the definition of J. Perez and A. Ros.

math.DG↗