Preprints

[01] F. Pacard and T. Sun. Doubling constructions for constant mean curvature hypersurfaces in Riemannian manifolds. pdf

Abstract :
Given an oriented minimal hypersurface S in a Riemannian manifold of dimension at least 3, we prove the existence of constant mean curvature hypersurfaces which have small mean curvature and which are double graphs over S. The constant mean curvature hypersurfaces we obtained can be understood as the connected sum at points of two copies of S. This result generalizes former results by A. Butscher and F. Pacard in the special case where the initial minimal surface is the Clifford torus in the sphere.


[02] W. Ao, M. Musso, F. Pacard and J. Wei. Solutions without any symmetry for semilinear elliptic problems. pdf

Abstract : We prove the existence of infinitely many solitary waves for the nonlinear Klein-Gordon or Schrödinger equation ∆u − u + u^3 = 0, in R^2 , which have finite energy and whose maximal group of symmetry reduces to the identity or is a discrete group. hedral group of isometries which leave a horizontal regular polygon with m + 1 sides.

Unpublished lecture notes

[01] F. Pacard. Lectures on "Connected sum constructions in geometry and nonlinear analysis". pdf

Abstract  : These are notes which cover the lectures I gave in the spring of 2006 in Roma I-La Sapienza and they also cover the lectures I gave in the spring of 2007 in the ETH for some Nachdiplomvorlesung. These lecture notes cover the analysis of some class of elliptic second order operators on manifolds with asymptotically periodic ends which appear in the analysis of some geometric problems : constant mean curvature surfaces, singular Yamabe problem, ... So far the first part is complete. They contain all the necessary information to understand the linear analysis for some class of ellitpic operators which are defined on manifolds with asymptotically periodic ends. 

The second part will contain applications of the results of the first part for the understanding of the theory of constant mean curvature surfaces, complete constant scalar curvature metrics and also some application to some singular perturbation problems. This part is not yet finished but I am working on it...and I will do my best to update the latest version on this web page.