相关论文: GJMS operators and Q-curvature for conformal Codaz…
We construct almost complex algebraic curvature tensors for pseudo Hermitian inner products whose skew-symmetric curvature operator has constant Jordan normal form on the set of non-degenerate complex lines.
We obtain a Principal Kinematic Formula and a Crofton Formula for surface area measures of convex bodies, both involving linear operators on the vector space of signed measures on the unit sphere $S^{d-1}$. These formulas are related to a…
The main goal of this paper is to present results of existence and non-existence of convex functions on Riemannian manifolds and, in the case of the existence, we associate such functions to the geometry of the manifold. Precisely, we prove…
As a continuation of \cite{NSY:local}, we mainly discuss the global structure of two-dimensional locally compact geodesically complete metric spaces with curvature bounded above. We first obtain the result on the Lipschitz homotopy…
Non-convex optimization plays a key role in a growing number of machine learning applications. This motivates the identification of specialized structure that enables sharper theoretical analysis. One such identified structure is…
In general relativity, an external observer cannot distinguish distinct internal structures between two spherically symmetric stars that have the same total mass $M$. However, when quantum corrections are taken into account, the external…
We investigate the conformal algebra on the fuzzy sphere, and in particular the generators of translations and special conformal transformations which are emergent symmetries in the infinite IR but are broken along the RG flow. We show how…
This paper consists of two parts. In the first part we show that in odd dimension, as well as in even dimension below the critical weight (i.e. half the dimension), the logarithmic singularities of Schwartz kernels and Green kernels of…
In this note we obtain a formula for the sectional curvature on an arbitrary two-dimensional smooth manifold $M$ equipped with a Lorentzian metric $g$.
For the minimal graph with strict convex level sets, we find an auxiliary function to study the Gaussian curvature of the level sets. We prove that this curvature function is a concave function with respect to the height of the minimal…
In this paper, the long-time existence and convergence results are derived for locally constrained flows with initial value some compact spacelike hypersurface that is suitably pinched in the de Sitter space. As applications, geometric…
In the paper we consider convex cones in infinite-dimensional real vector spaces which are endowed with no topology. The main purpose is to study an internal geometric structure of convex cones and to obtain an analytical description of…
We consider some natural connections which arise between right-flat (p, q) paraconformal structures and integrable systems. We find that such systems may be formulated in Lax form, with a "Lax p-tuple" of linear differential operators,…
This manuscript is devoted to constructing complete metrics with constant higher fractional curvature on punctured spheres with finitely many isolated singularities. Analytically, this problem is reduced to constructing singular solutions…
We investigate some properties of geometric operators in canonical quantum gravity in the connection approach \`a la Ashtekar, which are associated with volume, area and length of spatial regions. We motivate the construction of analogous…
In this article, we investigate deformation problems of $Q$-curvature on closed Riemannian manifolds. One of the most crucial notions we use is the $Q$-singular space, which was introduced by Chang-Gursky-Yang during 1990's. Inspired by the…
The main purpose of this paper is to introduce and investigate the notion of Jacobi-Jordan conformal algebra. They are a generalization of Jacobi-Jordan algebras which correspond to the case in which the formal parameter lambda equals 0. We…
Borrowing elementary ideas from solid mechanics and differential geometry, this presentation shows that the volume swept by a regular solid undergoing a wide class of volume-preserving deformations induces a rather natural metric structure…
We consider the problem of prescribing the Gaussian and the geodesic curvatures of a compact surface with boundary by a conformal deformation of the metric. We derive some existence results using a variational approach, either by…
We study numerical computation of conformal invariants of domains in the complex plane. In particular, we provide an algorithm for computing the conformal capacity of a condenser. The algorithm applies for wide kind of geometries: domains…