arXiv research

Extends symplectic reduction and theorem to Lie algebroids.

Proves a theorem similar to Moser's using a normalization method.

There are proven few analogues of the Theorem of Moser using The Approximation Theorem of Artin.

Moser's theorem (1965) states that the diffeomorphism group of a compact manifold acts transitively on the space of all smooth positive densities with fixed volume. Here we describe the extension of this result to manifolds with corners. In particular we obtain Moser's theorem on simplices. The proof is based on Banyag…

Theorems adapted for prequantum systems, showing symplectomorphism and gauge transformation.

Kuranishi's proof of complex deformation theory revisited

The abstract proves a Moser-like theorem for C-symplectic structures and applies it to complex manifolds.

New theorems prove uniqueness of solutions to geometric PDEs.

Researchers found counterexamples to a 2-jet determination theorem in higher codimension.

The paper proves symplectic neighbourhood theorems for stratified subspaces.

Sharp inequalities for radial functions on hyperbolic spaces without boundary conditions.

Gradient estimates for special harmonic functions on manifolds.

This thesis is divided into two parts. In the first part we study completely integrable systems, and their underlying structures, in detail. We study their deformation theory and the different equivalence relations surrounding it. We motivate the definition of weak equivalence (found in the literature) by studying diff…

Paper develops a weighted linearization approach for vector fields.

Second part of proving linearization theorem for sl2(C).

The paper constructs metrics on spheres with families of minimal hypersurfaces.

Study metric perturbations to make degenerate harmonic forms non-degenerate.

The paper studies gradient estimates for solutions of a nonlinear elliptic equation on Riemannian manifolds.

We provide sufficient conditions for the existence of Darboux charts on weakly symplectic bounded Fréchet manifolds by using the Moser's trick.

We show how the classical Moser Lemma from symplectic geometry extends to generalized complex structures (GCS) on arbitrary Courant algebroids. For this, we extend the notion of Lie derivative to sections of the tensor bundle $(\otimes^i E)\otimes(\otimes^j E^*)$ with respect to sections of the Courant algebroid $E$ us…

It is proven a new analogue of the Theorem of Moser in a generalized context defined by Shilov Boundaries of Bounded and Symmetric Domains.

By using Moser's iteration technique, we show some removable singularity theorem of the tension field for biharmonic maps into manifolds of non-positive curvature, and the bubbling theorem of biharmonic maps and also harmonic maps.

Sharp gradient estimates for a weighted p-Laplacian equation on metric measure spaces.

The paper establishes gradient estimates and Liouville theorems for Φ-Laplacian equations on Riemannian manifolds.

Proves the Hodge conjecture for complex projective manifolds.

We prove the following nonholonomic version of the classical Moser theorem: given a bracket-generating distribution on a connected compact manifold (possibly with boundary), two volume forms of equal total volume can be isotoped by the flow of a vector field tangent to this distribution. We describe formal solutions of…

The paper explores similarities in even and odd-dimensional geometry.

In this article, we first describe a normal form of real-analytic, Levi-nondegenerate submanifolds of $C^N$ of codimension d $\ge$ 1 under the action of formal biholomorphisms, that is, of perturbations of Levi-nondegenerate hyperquadrics. We give a sufficient condition on the formal normal form that ensures that the n…

We establish a regularity theorem for the Harmonic - Einstein Equation. As a byproduct of the local regularity, we also have a compactness theorem on Harmonic - Einstein equation. The method is mainly the Moser iteration technique which has been used and developed by \cite{BKN89}, \cite{Tian90}, \cite{TV05a} and others…

This paper is about the rigidity of compact group actions in the Poisson context. The main resut is that Hamiltonian actions of compact semisimple type are rigid. We prove it via a Nash-Moser normal form theorem for closed subgroups of SCI-type. This Nash-Moser normal form has other applications to stability results th…

Paper analyzes solutions to quasilinear elliptic equations on manifolds using Nash-Moser iteration.

We apply the Nash-Moser theorem for exact sequences of R. Hamilton to the context of deformations of Lie algebras and we discuss some aspects of the scope of this theorem in connection with the polynomial ideal associated to the variety of nilpotent Lie algebras. This allows us to introduce the space $H_{k-nil}^2(\math…

Uniform proof of Kähler-Einstein metrics with arbitrary polarizations.

The paper uses Nash-Moser iteration to prove gradient estimates for nonlinear equations on Riemannian manifolds.

We revisit the linearization theorems for proper Lie groupoids around general orbits (statements and proofs). In the the fixed point case (known as Zung's theorem) we give a shorter and more geometric proof, based on a Moser deformation argument. The passing to general orbits (Weinstein) is given a more conceptual inte…

Moser's Bernstein theorem \cite{moser61} says that an entire minimal graph of codimension 1 with bounded slope must be a hyperplane. An analogous result for arbitrary codimension is not true, by an example of Lawson-Osserman. Here, we show that Moser's theorem nevertheless extends to codimension 2, i.e., a minimal $p$-…

Local flatness theorem for paraquaternionic contact structures.

We introduce a new perspective on the classical Nirenberg problem of understanding the possible Gauss curvatures of metrics on $S^{2}$ conformal to the round metric. A key tool is to employ the smooth Cheeger-Gromov compactness theorem to obtain general and essentially sharp a priori estimates for Gauss curvatures $K$ …

The paper studies symplectic forms on projective limits of Banach bundles and their Darboux Theorem.

We give a local classification of generalized complex structures. About a point, a generalized complex structure is equivalent to a product of a symplectic manifold with a holomorphic Poisson manifold. We use a Nash-Moser type argument in the style of Conn's linearization theorem.

We prove Gray--Moser stability theorems for complementary pairs of forms of constant class defining symplectic pairs, contact-symplectic pairs and contact pairs. We also consider the case of contact-symplectic and contact-contact structures, in which the constant class condition on a one-form is replaced by the conditi…

Complex analytic sets' Lipschitz geometry at infinity characterized.

A geometric flow on $(2,2)$-forms is introduced which preserves the balanced condition of metrics, and whose stationary points satisfy the anomaly equation in Strominger systems. The existence of solutions for a short time is established, using Hamilton's version of the Nash-Moser implicit function theorem.

Paper proves constants for Moser-Trudinger inequality on surfaces.

Paper proves Liouville theorems for harmonic functions under specific curvature bounds.

After gluing foliated complex manifolds, we derive a preparation-like theorem for singularities of codimension one foliations and planar vector fields (in the real or complex setting). Without computation, we retrieve and improve results of Levinson-Moser for functions, Dufour-Zhitomirskii for non degenerate codimensio…

The paper studies deformations of symplectic groupoids using cohomology and spectral sequences.

On a doubling metric measure space endowed with a "carré du champ", we consider $L^p$ estimates $(G_p)$ of the gradient of the heat semigroup and scale-invariant $L^p$ Poincaré inequalities $(P_p)$. We show that the combination of $(G_p)$ and $(P_p)$ for $p\ge 2$ always implies two-sided Gaussian heat kernel bounds. Th…