相关论文: Optimal Synthesis in a Radially Symmetric Grushin …

In this paper, we propose and analyze a high-order finite volume method for the Poisson problem based on the reduced discontinuous Galerkin (RDG) space. The main idea is to employ the RDG space as the trial space and the piecewise constant…

In this work we develop the path integral optimization in a class of inhomogeneous 2d CFTs constructed by putting an ordinary CFT on a space with a position dependent metric. After setting up and solving the general optimization problem, we…

We prove that a globally hyperbolic smooth spacetime endowed with a $\smash{\mathrm{C}^1}$-Lorentzian metric whose Ricci tensor is bounded from below in all timelike directions, in a distributional sense, obeys the timelike…

We establish a global rigidity theorem for Riemannian metrics without conjugate points on three-manifolds of the form $M = \Sigma \times S^1$, where $\Sigma$ is a compact orientable surface of genus at least 2. The main result states that…

The spherically symmetric, static spacetime generated by a crossflow of non-interacting radiation streams, treated in the geometrical optics limit (null dust) is equivalent to an anisotropic fluid forming a radiation atmosphere of a star.…

We consider diagonal cylindrically symmetric metrics, with an interior representing a general non-rotating fluid with anisotropic pressures. An exterior vacuum Einstein-Rosen spacetime is matched to this using Darmois matching conditions.…

We study both function theoretic and spectral properties on complete noncompact smooth metric measure space $(M,g,e^{-f}dv)$ with nonnegative Bakry-\'{E}mery Ricci curvature. Among other things, we derive a gradient estimate for positive…

We derive the gravitational field and the spacetime metric generated by sources in quantum superposition of different locations. We start by working in a Newtonian approximation, in which the effective gravitational potential is computed as…

In this article, we present a gravitational collapse null dust solution of the Einstein field equations. The spacetime is regular everywhere except on the symmetry axis where it possesses a naked curvature singularity, and admits one…

The Gaussian-smoothed optimal transport (GOT) framework, recently proposed by Goldfeld et al., scales to high dimensions in estimation and provides an alternative to entropy regularization. This paper provides convergence guarantees for…

We study the matching of LRS spatially homogeneous collapsing dust space-times with non-stationary vacuum exteriors in cylindrical symmetry. Given an interior with diagonal metric we prove existence and uniqueness results for the exterior.…

We study some analytic properties of distance decreasing self-maps onto the complement of a smooth curve $\Sigma$ in $S^n$. For $n>4$ and $n\equiv 0 \mod 4$, let $\Sigma$ be an embedded circle in $S^n$ and let $g$ be a complete Riemannian…

Let X be a smooth complex projective variety, and let Y in X be a smooth very ample hypersurface such that -K_Y is nef. Using the technique of relative Gromov-Witten invariants, we give a new short and geometric proof of (a version of) the…

We show that a complete embedded maximal surface in the 3-dimensional Lorentz-Minkowski space $L^3$ with a finite number of singularities is, up to a Lorentzian isometry, an entire graph over any spacelike plane asymptotic to a vertical…

This work is a companion to [EJE1] and its purpose is threefold: first, we will establish local well-posedness for the axi-symmetric $3D$ Euler equation in the domains $\{(x_1,x_2,x_3) \in \mathbb{R}^3 : x_3^2 \le \mathfrak{c}(x_1^2 +…

It is shown that for any two compact metric spaces there exists an "optimal" correspondence which the Gromov-Hausdorff distance is attained at. Each such correspondence generates isometric embeddings of these spaces into a compact metric…

We prove that, given a compact Riemann surface $\Sigma$ and disjoint finite sets $\varnothing\neq E\subset\Sigma$ and $\Lambda\subset\Sigma$, every map $\Lambda \to \mathbb{R}^3$ extends to a complete conformal minimal immersion…

We study the observability properties of the Grushin equation with an inverse square potential, whose singularity occurs at the boundary of two-dimensional rectangular domains or in the interior of the domain in higher dimensions. In some…

In this paper we argue that the well-known maximal extensions of the Kerr and Kerr-Newman spacetimes characterized by a specific gluing (on disks) of two asymptotically flat regions with ADM masses of opposite signs are physically…

We present a maximally symmetric vacuum spacetime, which is locally isometric anti- de Sitter, admitting closed timelike curves appear after a definite instant of time i.e., a time-machine spacetime. The spacetime is regular, free-from…