Minimal surfaces and deformations of holomorphic curves in Kähler-Einstein manifolds
Minimizing Harmonic Mappings form a surface perfored with small holes into a riemannian manifold.
Modules pour les familles de courbes planes
L’étude des familles de courbes plane différentiables se ramène a celle des diagrammesoù est une surface, et étant différentiables. Dans la classification de ces diagrammes à équivalence près il apparaît trois types de modules: des modules locaux attachés à chaque fronce de , des modules semi-locaux attachés à la superposition en un même point de plusieurs situations locales, des modules globaux attachés aux “courbes de contact” le long desquelles certaines courbes sont tangentes. Nous explicitons...
Monge-Ampère equations and surfaces with negative Gaussian curvature
In [24], we studied the singularities of solutions of Monge-Ampère equations of hyperbolic type. Then we saw that the singularities of solutions do not coincide with the singularities of solution surfaces. In this note we first study the singularities of solution surfaces. Next, as the applications, we consider the singularities of surfaces with negative Gaussian curvature. Our problems are as follows: 1) What kinds of singularities may appear?, and 2) How can we extend the surfaces beyond the singularities?...
Monodromy Groups of Critical Point of Functions.
Monodromy of functions defined on isolated singularities of complete intersections
Monotonicity of first eigenvalues along the Yamabe flow
We construct some nondecreasing quantities associated to the first eigenvalue of
More on the Determinacy of Smooth Map-Germs.
Morrey-Campanato spaces on manifolds
Morse-Bott functions with two critical values on a surface
We study Morse-Bott functions with two critical values (equivalently, nonconstant without saddles) on closed surfaces. We show that only four surfaces admit such functions (though in higher dimensions, we construct many such manifolds, e.g. as fiber bundles over already constructed manifolds with the same property). We study properties of such functions. Namely, their Reeb graphs are path or cycle graphs; any path graph, and any cycle graph with an even number of vertices, is isomorphic to the Reeb...
Morse-Sard theorem in infinite dimensional Banach spaces and investigation of the set of all critical levels
Moser's Implicit Function Theorem in the Framework of Analytic Smoothing.
Mountain pass theorems and global homeomorphism theorems
M-T topologically stable mappings are uniformly stable.
Multiple perturbed solutions near nondegenerate manifolds of solutions
The existence of multiple solutions for perturbed equations is shown near a manifold of solutions of an unperturbed equation via the Nielsen fixed point theory.
Nash-Moser techniques for nonlinear boundary-value problems.
Natural Lagrangian structures
Natural pseudodistances between closed surfaces
Let us consider two closed surfaces , of class and two functions , of class , called measuring functions. The natural pseudodistance between the pairs , is defined as the infimum of as varies in the set of all homeomorphisms from onto . In this paper we prove that the natural pseudodistance equals either , , or , where and are two suitable critical values of the measuring functions. This shows that a previous relation between the natural pseudodistance and critical values...
Necessary and sufficient conditions for a curve to be the gradient range of a -smooth function.
Necessary Conditions for Multiple Integral Problem in the Calculus of Variations.