Related papers: The Morse index theorem for mechanical systems wit…

We develop the idea of self-indexing and the technology of gradient-like vector fields in the setting of Morse theory on a complex algebraic stratification. Our main result is the local existence, near a Morse critical point, of…

Using a central limit theorem for arrays of interacting quantum systems, we give analytical expressions for the density of states and the partition function at finite temperature of such a system, which are valid in the limit of infinite…

Local action principles on a manifold $\M$ are invariant (if at all) only under diffeomorphisms that preserve the boundary of $\M$. Suppose, however, that we wish to study only part of a system described by such a principle; namely, the…

We present sufficient conditions for the existence of a periodic solution for a class of systems describing the periodically forced motion of a massive point on a compact surface with a boundary.

We prove a theorem of uppersemicontinuity for the metric entropy of meromorphic maps.

In this short note we would like to show how it is possible to use techniques introduced in the theory of local dynamics of holomorphic germs tangent to the identity to study global meromorphic self-maps of the complex projective space. In…

On a smooth asymptotically flat Riemannian manifold with non-compact boundary, we prove a positive mass theorem for metrics which are only continuous across a compact hypersurface. As an application, we obtain a positive mass theorem on…

We found a necessary and sufficient condition for the existence of the tensor product of modules over a vertex algebra. We defined the notion of vertex bilinear map and we provide two algebraic construction of the tensor product, where one…

First, we prove a theorem on dynamics of actions of monoids by endomorphisms of semigroups. Second, we introduce algebraic structures suitable for formalizing infinitary Ramsey statements and prove a theorem that such statements are implied…

We prove an index theorem for inhomogeneous differential operators satisfying the Rockland condition (hence hypoelliptic). This theorem extends an index theorem for contact manifolds by Van-Erp.

We study a new approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. Our approach is based on the minimization of an integral functional arising from a volume integral formulation of the…

Computational Group Theory is applied to indexed objects (tensors, spinors, and so on) with dummy indices. There are two groups to consider: one describes the intrinsic symmetries of the object and the other describes the interchange of…

Inspired by work of Ejiri-Micallef on closed minimal surfaces, we compare the energy index and the area index of a free-boundary minimal surface of a Riemannian manifold with boundary, and show that the area index is controlled from above…

Let $G$ be a torus and $M$ a compact Hamiltonian $G$-manifold with finite fixed point set $M^G$. If $T$ is a circle subgroup of $G$ with $M^G=M^T$, the $T$-moment map is a Morse function. We will show that the associated Morse…

We prove an Ahlfors refection theorem for $p$-reflections over Jordan curves bounding subhyperbolic domains in $\hat {\mathbb C}$.

We prove a centre manifold theorem for a map along a manifold-with-boundary of fixed points, and provide an application to the study of gradient descent with large step size on two-layer matrix factorisation problems.

In this work, we prove a version of the fundamental theorem of submanifolds to target manifolds with warped structure.

We provide a rigorous justication of nonlinear geometric optics expansions for reflecting \emph{pulses} in space dimensions $n>1$. The pulses arise as solutions to variable coefficient semilinear first-order hyperbolic systems. The…

Open discrete mappings with a modulus condition in metric spaces are considered. Some results related to local behavior of mappings as well as theorems about continuous extension to a boundary are proved.

We show some simple sufficient conditions for which the multilinear embedding theorem holds for fractional sparse operators. By verifying these conditions, we establish the theorem for power weights. We also provide Morrey-type sufficient…