Related papers: The Morse-Bott-Kirwan condition is local

We establish Ecalle's mould calculus in an abstract Lie-theoretic setting and use it to solve a normalization problem, which covers several formal normal form problems in the theory of dynamical systems. The mould formalism allows us to…

Here we prove the necessary analytic results to construct a Morse theory for the Yang-Mills-Higgs functional on the space of Higgs bundles over a compact Riemann surface. The main result is that the gradient flow with initial conditions…

We prove that the ground state for the Dirac equation on Minkowski space in static, smooth external potentials satisfies the Hadamard condition. We show that it follows from a condition on the support of the Fourier transform of the…

Using the notion of equivariant Kirwan map, as defined by Goldin, we prove that -- in the case of Hamiltonian torus actions with isolated fixed points -- Tolman and Weitsman's description of the kernel of the Kirwan map can be deduced…

We develop a globalized Proximal Newton method for composite and possibly non-convex minimization problems in Hilbert spaces. Additionally, we impose less restrictive assumptions on the composite objective functional considering…

It is a theorem of Kim-Tamagawa that the $\mathbb Q_\ell$-pro-unipotent Kummer map associated to a smooth projective curve $Y$ over a finite extension of $\mathbb Q_p$ is locally constant when $\ell\neq p$. The present paper establishes two…

We derive the complete orbit of boundary conditions for supergravity models which is closed under the action of all local symmetries of these models, and which eliminates spurious field equations on the boundary. We show that the…

In this paper, we propose a new method that combines the inexact Newton method with a procedure to obtain a feasible inexact projection for solving constrained smooth and nonsmooth equations. The local convergence theorems are established…

In this paper, we investigate the geometric invariant properties of a normal curve on a smooth immersed surface under conformal transformation. We obtain an invariant-sufficient condition for the conformal image of a normal curve. We also…

We provide some explicit examples wherein the Schr\"odinger equation for the Morse potential remains exactly solvable in a position-dependent mass background. Furthermore, we show how in such a context, the map from the full line $(-…

It is well known that any measure in S^2 satisfying certain simple conditions is the surface measure of a bounded convex body in R^3. It is also known that a local perturbation of the surface measure may lead to a nonlocal perturbation of…

We develop functoriality for Morse theory, namely, to a pair of Morse-Smale systems and a generic smooth map between the underlying manifolds we associate a chain map between the corresponding Morse complexes, which descends to the correct…

In this paper, we study Lipschitz-Fredholm vector fields on Bounded-Fr\'{e}chet-Finsler manifolds. In this context we generalize the Morse-Sard-Brown theorem, asserting that if $M$ is a connected smooth bounded-Fr\'{e}chet-Finsler manifold…

In a soliton sector of a quantum field theory, it is often convenient to expand the quantum fields in terms of normal modes. Normal mode creation and annihilation operators can be normal ordered, and their normal ordered products have…

Let W be a smooth complex quasiprojective variety with the action of a connected reductive group G. Adapting the stratification approach of Teleman to a microlocal context, we prove a vanishing theorem for the functor of G-invariant…

The motion of a system of particles under electromagnetic interaction is considered. Under the assumption that the force acting on an electric charge is given by the sum of the electromagnetic fields produced by any other charged particles…

In this article, we show that (i) any smooth function on compact Riemann surface with non-empty smooth boundary $ (M, \partial M, g) $ can be realized as a Gaussian curvature function; (ii) any smooth function on $ \partial M $ can be…

Using the standard canonical formalism, the equations of mechanics and kinetics in the Friedmann-Lemaitre-Robertson-Walker (FLRW) space-times in Cartesian coordinates have been obtained. The transformation law of the generalized momentum…

In this work, we study a gap phenomenon in locally conformally flat Riemannian manifolds with non-negative Ricci curvature. We construct complete solutions to the Yamabe flow that exhibit instantaneous bounded curvature as they evolve.…

We consider the Euler-Korteweg system with space periodic boundary conditions $ x \in \mathbb T^d $. We prove a local in time existence result of classical solutions for irrotational velocity fields requiring natural minimal regularity…