Related papers: Stokes Theorem for Lipschitz forms on a smooth man…

A famous result of Jurgen Moser states that a symplectic form on a compact manifold cannot be deformed within its cohomology class to an inequivalent symplectic form. It is well known that this does not hold in general for noncompact…

We establish for smooth projective real curves the equivalent of the classical Clifford inequality known for complex curves. We also study the cases when equality holds.

In this paper, we show Langton's type theorem on separatedness and properness of moduli functor of torsion free semistable sheaves on algebraic orbifolds over an algebraically closed field k

The convex cone $SC_{\mathrm{SLip}}^1(\mathcal{X})$ of real-valued smooth semi-Lipschitz functions on a Finsler manifold $\mathcal{X}$ is an order-algebraic structure that captures both the differentiable and the quasi-metric feature of…

The well known $g$-conjecture for homology spheres follows from the stronger conjecture that the face ring over the reals of a homology sphere, modulo a linear system of parameters, admits the strong-Lefschetz property. We prove that the…

We prove a gluing theorem for a symplectic vortex on a compact complex curve and a collection of holomorphic sphere bubbles. Using the theorem we show that the moduli space of regular stable symplectic vortices on a fixed curve with varying…

A simple analytic proof of the formula known as the non-Abelian Stokes theorem is given. It is explicitly shown that the consistency of the formula is guaranteed by the Bianchi identity for the gauge field. An attempt is made to construct…

We prove a Livsic type theorem for cocycles taking values in groups of diffeomorphisms of low-dimensional manifolds. The results hold without any localization assumption and in very low regularity. We also obtain a general result (in any…

We prove that, given a planar bi-Lipschitz homeomorphism $u$ defined on the boundary of the unit square, it is possible to extend it to a function $v$ of the whole square, in such a way that $v$ is still bi-Lipschitz. In particular,…

A general local center manifold theorem around stationary trajectories is proved for nonlinear cocycles acting on measurable fields of Banach spaces.

We establish two results concerning a class of geometric rough paths $\mathbf{X}$ which arise as Markov processes associated to uniformly subelliptic Dirichlet forms. The first is a support theorem for $\mathbf{X}$ in $\alpha$-H\"older…

Using recent developments in the theory of mixed motives, we prove that the log Bloch conjecture holds for an open smooth complex surface if the Bloch conjecture holds for its compactification. This verifies the log Bloch conjecture for all…

We prove a homological stability theorem for moduli spaces of high-dimensional, highly connected manifolds, with respect to forming the connected sum with the product of spheres $S^{p}\times S^{q}$, for $p < q < 2p - 2$. This result is…

A smooth map having only fold singularities is called a fold-map. We will give effective conditions for a continuous map to be homotopic to a fold-map from the viewpoint of the homotopy principle.

We prove that the displacement problem of inhomogeneous elastostatics in a two--dimensional exterior Lipschitz domain has a unique solution with finite Dirichlet integral $\u$, vanishing uniformly at infinity if and only if the boundary…

We prove the Myers-Steenrod theorem for local topological groups of isometries acting on pointed $\mathcal{C}^{k,\alpha}$-Riemannian manifolds, with $k+\alpha>0$. As an application, we infer a new regularity result for a certain class of…

Since a Poisson Structure is a smooth bivector field, we use a ring-valued sheaf $\OO_{X}$ on a manifold with corners $X$, we can interpret $\OO_{X}(U)$ as the ring of admissible smooth functions where $U$ is an open subset on $X$, in this…

We give two generalizations of the Clifford theorem to algebraic surfaces. As an application, we obtain some bounds for the number of moduli of surfaces of general type.

Away from the central axis, we prove the stability of the Positive Mass Theorem in the $W^{1,p}$ sense for asymptotically flat axisymmetric manifolds with nonnegative scalar curvature satisfying some additional technical assumptions. We…

We show that a necessary and sufficient condition for a smooth function on the tangent bundle of a manifold to be a Lagrangian density whose action can be minimized is, roughly speaking, that it be the sum of a constant, a nonnegative…