arXiv research

In this paper we study the behavior of solutions of a second order differential equation. The existence of a zero and its localization allow us to get some compactness results. In particular we obtain a Myers' type theorem even in the presence of an amount of negative curvature. The technique we use also applies to the…

Paper proves Horowitz-Myers conjecture in 3-7 dimensions.

This paper completes the classification of S1-symmetric static vacuum black holes.

Constructs metrics with negative constant scalar curvature.

Proves a sharp inequality for toroidal surfaces in Horowitz-Myers geon.

The paper extends Bonnet-Myers theorems using Bakry-Emery Ricci curvature.

Proves a local version of Myers-Steenrod theorem for specific manifolds.

We introduce the notion of Bonnet-Myers and Lichnerowicz sharpness in the Ollivier Ricci curvature sense. Our main result is a classification of all self-centered Bonnet-Myers sharp graphs (hypercubes, cocktail party graphs, even-dimensional demi-cubes, Johnson graphs $J(2n,n)$, the Gosset graph and suitable Cartesian …

The paper extends Bonnet-Myers theorem for manifolds with nonnegative Ricci curvature.

Generalizes Bonnet-Myers theorem with small Kato constant.

The extrinsic Bonnet-Myers theorem is proven for positive Ricci curvature manifolds.

We give a complementary generalization of the extensions of Bonnet-Myers theorem obtained by Calabi and also Cheeger-Gromov-Taylor.

In this paper we prove a new Myers' type diameter estimate on a complete connected Reimannian manifold which admits a bounded vector field such that the Bakry-Émery Ricci tensor has a positive lower bound. The result is sharper than previous Myers' type results. The proof uses the generalized mean curvature comparison …

The paper calculates graph Ricci curvature and finds properties of specific graph types.

In this paper we introduce an algorithm to determine the equivalence of five dimensional spacetimes, which generalizes the Karlhede algorithm for four dimensional general relativity. As an alternative to the Petrov type classification, we employ the alignment classification to algebraically classify the Weyl tensor. To…

Sharp spectral theorems and isoperimetric inequalities for manifolds with nonnegative Ricci curvature.

This is the second article of a series or two, proving a generalisation of the uniqueness theorem of the Schwarzschild solution. The theorem to be shown classifies all (metrically complete) solutions of the static vacuum Einstein equations with compact but non-necessarily connected horizon without any further assumptio…

The celebrated uniqueness's theorem of the Schwarzschild solution by Israel, Robinson et al, and Bunting/Masood-ul-Alam, asserts that the only asymptotically flat static solution of the vacuum Einstein equations with compact but non-necessarily connected horizon is Schwarzschild. Between this article and its sequel we …

Bonnet-Myers theorem applied to Q-curvature on 4-manifolds.

The paper proves a compactness theorem for spaces with Bakry-Emery Ricci tensor.

The study proves a new positive energy theorem for manifolds with specific curvature properties.

In this paper,we prove the following Myers-type theorem: if $(M^n,g)$, $n\geq 3$, is an n-dimensional complete locally conformally flat Riemannian manifold with bounded Ricci curvature satisfying the Ricci pinching condition $Rc\geq εRg>0$, where $ε>0$ is an uniform constant, then $M^n$ must be compact.

Proves closure for specific spacetimes with certain conditions.

Higher-dimensional spacetimes have well-behaved boundaries.

New Alexandrov-Patchwork construction for Lorentzian spaces with curvature bounds.

The study proves a compactness theorem for manifolds with specific curvature conditions.

Paper uses language models to predict MBTI personality types with high accuracy.

We prove a Bonnet-Myers type theorem for quaternionic contact manifolds of dimension bigger than 7. If the manifold is complete with respect to the natural sub-Riemannian distance and satisfies a natural Ricci-type bound expressed in terms of derivatives up to the third order of the fundamental tensors, then the manifo…

The Bakry-Émery-Ricci tensor is extended and comparison theorems are proven.

In this note we prove convexity, in the sense of Colding-Naber, of the regular set of solutions to some complex Monge-Ampere equations with conical singularities along simple normal crossing divisors. In particular, any two points in the regular set can be joined by a smooth minimal geodesic lying entirely in the regul…

Maximal diameter theorem for graphs with positive Ricci curvature.

Proves positive energy conjecture for a specific metric class.

Study on Kähler Finsler manifolds with curvature bounds, proving theorems.

The paper proves compactness theorems for specific types of tensors.

The paper refines Steinerberger curvature for block graphs and bridges.

Study compares H-type sub-Riemannian manifolds using uniform metrics.

New black hole solutions cannot be rotated without breaking their structure.

New curvature measure on graphs improves diameter and eigenvalue bounds.

We prove a family of new Weitzenböck formulas on a Riemannian foliation with totally geodesic leaves. These Weitzenböck formulas are naturally parametrized by the canonical variation of the metric. As a consequence, under natural geometric conditions, the horizontal Laplacian satisfies a generalized curvature dimension…

We introduce some new curvature quantities such as conformal Ricci curvature and bi-Ricci curvature and extend the classical Myers theorem under these new curvature conditions. Moreover, we are able to obtain the Myers type theorem for minimal submanifolds in ambient manifolds with positive bi-Ricci curvature. Some top…

New proofs confirm travel time data determine simple metrics on a disc.

Harmonic coordinates for Finsler manifolds prove a theorem but not optimal regularity.

The paper proves new comparison theorems for sub-Laplacian in foliations with minimal leaves.

This paper explores charged black holes in 3+1 dimensions, finding limitations on their existence.

The paper confirms the existence of 5D regular static vacuum solutions with multiple black holes and Kasner asymptotics.

In this paper, we study the integral curvatures of Finsler manifolds and prove several Myers type theorems.

We prove a version of Myers-Steenrod's theorem for Finsler manifolds under minimal regularity hypothesis. In particular we show that an isometry between $C^{k,α}$-smooth (or partially smooth) Finsler metrics, with $k+α>0$, $k\in \mathbb{N} \cup \{0\}$, and $0 \leq α\leq 1$ is necessary a diffeomorphism of class $C^{k+1…

Study proves inequality linking black hole properties and angular momentum.