Related papers: On singular Q-curvature type equations
We consider conformal metrics of constant curvature 1 on a Riemann surface, with finitely many prescribed conic singularities and prescribed angles at these singularities. Especially interesting case which was studied by C. L. Chai, C. S…
The aim of this work is to establish the existence, uniqueness and q-Gevrey character of formal power series solutions of q-analogues of analytic doubly-singular equations. Using a new family of Nagumo norms adapted for q-differences we…
We aim to explore if inside a quantum vertex algebras, we can find the right notion of a quantum conformal algebra.
Normally one assumes isolated surface singularities to be normal. The purpose of this paper is to show that it can be useful to look at nonnormal singularities. By deforming them interesting normal singularities can be constructed, such as…
We study initial value problems for various geometric equations on a cohomogeneity manifold near a singular orbit. We show that when prescribing the Ricci curvature, or finding solutions to the Einstein and soliton equations, there exist…
We extend some results known for the K\"ahler-Ricci flow to the Chern-Ricci flow regarding the independence of singularity types for long-time solutions. Specifically, we show that if a solution to the Chern-Ricci flow exists with uniformly…
We establish several inequalities for manifolds with positive scalar curvature and, more generally, for the scalar curvature bounded from below, in the spirit of the classical bound on the distances between conjugates points in surfaces…
Generic self-gravitating quantum solutions that are not critically dependent on the specifics of microscopic interactions are presented. The solutions incorporate curvature effects, are consistent with the universality of gravity, and have…
We establish near-optimal quantitative uniqueness of continuation for solutions of evolution equations vanishing on the lateral boundary. These results were obtained simply by combining existing observability inequalities and energy…
We give a $\delta$-constant criterion for equinormalizability of deformations of isolated (not necessarily reduced) curve singularities over smooth base spaces of dimension $\geq 1$. For one-parametric families of isolated curve…
We discuss the existence of equilibrium configurations for the Hamiltonian point-vortex model on a closed surface $\Sigma$. The topological properties of $\Sigma$ determine the occurrence of three distinct situations, corresponding to…
We give necessary and sufficient conditions on the singular Bj\"{o}rling data to the singular Bj\"{o}rling problem's solution has a prescribed nature of singularity. As an application, we prove that near a maxface with a particular type of…
We investigate static, spherically symmetric solutions in gravitational theories which have limited curvature invariants, aiming to remove the singularity in the Schwarzschild space-time. We find that if we only limit the Gauss-Bonnet term…
In this article we prove the existence of solutions to the singular coagulation equation with multifragmentation. We use weighted $L^1$-spaces to deal with the singularities and to obtain regular solutions. The Smoluchowski kernel is…
In this paper, we consider a family of closed hypersurfaces which shrink self-similarly with speed of quotient curvatures. We show that the only such hypersurfaces are shrinking spheres.
In this paper we focus on various aspects of singular complex plane curves, mostly in the context of their homological properties and the associated combinatorial structures. We formulate some challenging open problems that can point to new…
The purpose of this work is to investigate the consequences of quantum gravity for the singularity problem. We study the higher-derivative terms that invariably appear in any quantum field theoretical model of gravity, handling them both…
We give some estimate of type sup*inf for scalar curvature type equations.
We define a new finite type invariant for stably homeomorphic class of curves on compact oriented surfaces without boundaries and extend to a regular homotopy invariant for spherical curves.
In this paper we give an explicit representation of the solutions of a characteristic Cauchy problem for a class of PDEs with singular coefficients. We give the explicit solutions in terms of the Gauss hypergeometric functions, which enable…