arXiv research

The study examines Ricci solitons and curvature inheritance on Robinson-Trautman spacetimes.

Curvature bounds preserved in length-minimizing disks.

The paper examines geometric properties of a unique spacetime model.

Curvature of 2D subsets preserved in their space.

Study on surface geometry in Lie groups with CR structures.

In this article, I prove that full subcomplexes of CAT(0) simplicial 3-complexes inherit the non positive curvature condition, and describe a family of counterexamples that prove this result can not be extended to higher dimensions.

We show that the configuration space over a manifold M inherits many curvature properties of the manifold. For instance, we show that a lower Ricci curvature bound on M implies for the configuration space a lower Ricci curvature bound in the sense of Lott-Sturm-Villani, the Bochner inequality, gradient estimates and Wa…

In homogenous space Sol we study compact surfaces with constant mean curvature and with non-empty boundary. We ask how the geometry of the boundary curve imposes restrictions over all possible configurations that the surface can adopt. We obtain a flux formula and we establish results that assert that, under some restr…

The present paper describes a way to relate Martin boundaries on spaces of varying topology. This enables us to approach some detailed inductive analysis of the eigenfunctions of conformal Laplacians on minimal hypersurfaces near their singularities. This can directly be used resp. translated to understand the way how …

Let M be a simply connected Riemannian symmetric space, with at most one flat direction. We show that every Riemannian (or unitary) vector bundle with parallel curvature over M is an associated vector bundle of a canonical principal bundle, with the connection inherited from the principal bundle. The problem of finding…

Diagnosing an inherited disease often requires identifying the pattern of inheritance in a patient's family. We represent family trees with genetic patterns of inheritance using hypergraphs and latent state space models to provide explainable inheritance pattern predictions. Our approach allows for exact causal inferen…

This note analyzes the normal form of gradient Ricci 4-solitons.

We prove that a H-surface M in H^2xR, |H| <= 1/2, inherits the symmetries of its boundary when the boundary is either a horizontal curve with curvature greater than one or two parallel horizontal curves with curvature greater than one, whose distance is greater or equal to πFurthermore we prove that the asymptotic boun…

We derive a local curvature estimate for four-dimensional stationary solutions to the inheriting Einstein-Maxwell-Klein-Gordon equations. In particular, it implies that any such stationary geodesically complete solution with vanishing Poynting vector and proper coupling constants (like dark energy) is flat. We also gen…

Parallel unlearning framework for inherited models reduces computational overhead.

In a previous article, we defined a very flexible notion of suborbifold and characterized those suborbifolds which can arise as the images of orbifold embeddings. In particular, suborbifolds are images of orbifold embeddings precisely when they are saturated and split. This article addresses the problem of orbifold str…

In this article we prove two non-existence results for translating solitons of the mean curvature flow (translators for short) in $\mathbb{R}^{m+1}$. We also obtain an upper bound to the maximum height that a compact embedded translator in $\mathbb{R}^{3}$ can achieve. On the other hand, we study graphical perturbation…

Block and Weinberger show that an arithmetic manifold can be endowed with a positive scalar curvature metric if and only if its $\rationals$-rank exceeds 2. We show in this article that these metrics are never in the same coarse class as the natural metric inherited from the base Lie group. Furthering the coarse $C^\as…

We prove that Maxwell fields of asymptotically flat solutions of the Einstein-Maxwell equations inherit the stationarity of the metric.

The key condition A3w of Ma, Trudinger and Wang for regularity of optimal transportation maps is implied by the nonnegativity of a pseudo-Riemannian curvature -- which we call cross-curvature -- induced by the transportation cost. For the Riemannian distance squared cost, it is shown that (1) cross-curvature nonnegativ…

We define a complex connection on a real hypersurface of $\C^{n+1}$ which is naturally inherited from the ambient space. Using a system of Codazzi-type equations, we classify connected real hypersurfaces in $\C^{n+1}$, $n\ge 2$, which are Levi umbilical and have non zero constant Levi curvature. It turns out that such …

Symmetric hypersurfaces and boundaries in R^n+1 with group actions.

In this work we study solutions of the prescribed mean curvature equation over a general domain that do not necessarily attain the given boundary data. To such a solution, we can naturally associate a current with support in the closed cylinder above the domain and with boundary given by the prescribed boundary data an…

Study non-degenerate anisocurved surfaces in homogeneous 3-manifolds.

Study shows how discrete graph curvature relates to manifold curvature.

The paper extends Liebmann's Theorem to convex hypersurfaces with boundary.

Adversarial robustness improved by sparsity in network weights.

Invariant reduction preserves Poisson structures in PDEs.

Model projection transfers convolutional network properties to feedforward networks.

Researchers infer gene activity in dividing cells, accounting for protein inheritance and division history.

The paper explores conditions for symmetries in Weingarten surfaces.

This paper studies how key tensor properties are inherited in subtensors of tensor train decompositions.

Symmetries of bundle gerbes modeled using multiplicative vector fields.

Kähler manifold loop space inherits Kähler structure and is complete.

Spacelike surfaces in the Lorentz-Minkowski space L^3 can be endowed with two different Riemannian metrics, the metric inherited from L^3 and the one induced by the Euclidean metric of R^3. It is well known that the only surfaces with zero mean curvature with respect to both metrics are open pieces of the helicoid and …

Proposes a variational NNCC formulation for infinite dimensions.

Study explores geometric properties of Vaidya-Bonner-de Sitter spacetime.

The paper examines geometric properties of a specific black hole spacetime.

We show that an open subset ${\mathfrak F}_4''$ of the ${\rm PU}(2,1)$ configuration space of four points in $S^3$ is in bijection with an open subset of %with a Kähler structure which is inherited from the one of ${\mathfrak H}^{\star}\times\mathbb{R}_{>0}$, where ${\mathfrak H}^\star$ is the affine-rotational group. …

A $λ$-translating soliton with density vector $\vec{v}$ is a surface $Σ$ in Euclidean space ${\mathbb R}^3$ whose mean curvature $H$ satisfies $2H=2λ+\langle N,\vec{v}\rangle$, where $N$ is the Gauss map of $Σ$. In this article we study the shape of a compact $λ$-translating soliton in terms of its boundary. If $Γ$ is …

Over the years, several studies have demonstrated that there exist significant disparities in health indicators in the United States population across various groups. Healthcare expense is used as a proxy for health in algorithms that drive healthcare systems and this exacerbates the existing bias. In this work, we foc…

Blowups of Kähler manifolds with extremal metrics inherit such metrics under stability conditions.

Let n>1 and G be the group SU(n) or Sp(n). This paper constructs compact symplectic manifolds whose symplectic quotient under a Hamiltonian G-action does not inherit the strong Lefschetz property.

We prove that any compact Kähler manifold bearing a holomorphic Cartan geometry contains a rational curve just when the Cartan geometry is inherited from a holomorphic Cartan geometry on a lower dimensional compact Kähler manifold.

Endowed with quotient topology inherited from the space of based loops, the fundamental group of the Hawaiian earring fails to be metrizable. The fundamental group of any space which retracts to the Hawaiian earring is also nonmetrizable.

We construct helicoid-like embedded minimal disks with axes along self-similar curves modeled on logarithmic spirals. The surfaces have a self-similarity inherited from the curves and the nature of the construction. Moreover, inside of a "logarithmic cone", the surfaces are embedded.

The study of Bonnet surfaces in 4D space forms reveals new conformally invariant properties and characterizes proper Bonnet surfaces.

Study of quasi-Kähler metrics on complex manifolds linked to c-projective metrizability.