arXiv research

Ancient solutions to Ricci flow on torus bundles have additional symmetries.

Identity testing for reversible Markov chains without symmetry assumption.

Metric evaluates symmetry-breaking in datasets, revealing severe biases.

New method detects symmetries beyond affine transformations.

The paper proves a numerical condition for solving complex Hessian quotient equations with Calabi symmetry.

We consider the classical "Serrin symmetry result" for the overdetermined boundary value problem related to the equation $Δu=-1$ in a model manifold of non-negative Ricci curvature. Using an extension of the Weinberger classical argument we prove a Euclidean symmetry result under a suitable "compatibility" assumption b…

This paper is centred on solving differential equations by symmetry groups for first order ODEs and is in response to Starrett (2007). It also explores the possibility of averting the assumptions by Olver (2000) that, in practice finding the solutions of the linearized symmetry condition is usually a much more difficul…

New Einstein metrics found on orthogonal groups without natural reductivity.

Study fixed angle inverse scattering with Riemannian metrics, proving uniqueness and stability.

Investigates geometric mean reversion process using Lie symmetry method.

We prove some existence results for the Webster scalar curvature problem on the Heisenberg group and on the unit sphere of ${\mathbb C}^{n+1}$, under the assumption of some natural symmetries of the prescribed curvatures. We use variational and perturbation techniques.

Study neckpinch singularities in Ricci flow with cylindrical symmetry.

We prove that under certain assumptions a partial differential equation can be derived from a variational principle. It is well-known from Noether's theorem that symmetries of a variational functional lead to conservation laws of the corresponding Euler-Lagrange equation. We reverse this statement and prove that a diff…

For compact Kählerian manifolds, the holomorphic pseudosymmetry reduces to the local symmetry if additionally the scalar curvature is constant and the structure function is non-negative. Similarly, the holomorphic Ricci-pseudosymmetry reduces to the Ricci-symmetry under these additional assumptions. We construct exampl…

Under weak regularity assumptions, only, we develop a fully geometric theory of vacuum Einstein spacetimes with T2 symmetry, establish the global well-posedness of the initial value problem for Einstein's field equations, and investigate the global causal structure of the constructed spacetimes. Our weak regularity ass…

This work presents a geometrical formulation of the Clairin theory of conditional symmetries for higher-order systems of partial differential equations (PDEs). We devise methods for obtaining Lie algebras of conditional symmetries from known conditional symmetries, and unnecessary previous assumptions of the theory are…

Solvable structures, likewise solvable algebras of local symmetries, can be used to integrate scalar ODEs by quadratures. Solvable structures, however, are particularly suitable for the integration of ODEs with a lack of local symmetries. In fact, under regularity assumptions, any given ODE always admits solvable struc…

Data symmetries in neural networks can generate conserved quantities.

Proves conjecture about sphere widths under rotational symmetry.

New equations use Pin(2) symmetry to study spinor and connection solutions.

Develops a theory for equivariant networks with partial domain symmetry.

Proposes learning invariances in neural networks using a weight-space approach.

The paper studies symmetries in quandles and their relative versions.

Geometric framework for dynamic feedback linearization of control systems with symmetry.

We study sharp asymptotics of the first eigenvalue on Riemannian surfaces obtained from a fixed Riemannian surface by attaching a collapsing flat handle or cross cap to it. Through a careful choice of parameters this construction can be used to strictly increase the first eigenvalue normalized by area if the initial su…

This work extends PAC-Bayesian learning guarantees to non-compact symmetries and non-invariant data.

We prove that if a closed, smooth, simply-connected 4-manifold with a circle action admits an almost non-negatively curved sequence of invariant Riemannian metrics, then it also admits a non-negatively curved Riemannian metric invariant with respect to the same action. The same is shown for torus actions of higher rank…

We generalize the Weinstein-Moser theorem on the existence of nonlinear normal modes (i.e., periodic orbits) near an equilibrium in a Hamiltonian system to a theorem on the existence of relative periodic orbits near a relative equilibrium in a Hamiltonian system with continuous symmetries. More specifically we signific…

Study manifolds with positive intermediate Ricci curvature and large symmetry rank.

The paper proves conjectures about Minkowski norms with specific symmetry groups.

In this paper we study symmetries, Newtonoid vector fields, conservation laws, Noether's Theorem and its converse, in the framework of the $k$-symplectic formalism, using the Frölicher-Nijenhuis formalism on the space of $k^1$-velocities of the configuration manifold. For the case $k=1$, it is well known that Cartan sy…

Classifies SL(n) covariant matrix-valued valuations on Lp-spaces.

The study proves rotationally symmetric property of certain shrinking gradient Yamabe solitons.

In a previous article, analytic 1-submanifolds had been classified w.r.t. their symmetry under a given regular and separately analytic Lie group action on an analytic manifold. It was shown that such an analytic 1-submanifold is either free or (via the exponential map) analytically diffeomorphic to the unit circle or a…

Solves Christoffel-Minkowski problem and Hessian equations with radial symmetry.

Introduces a variational framework for indefinite Lagrangians with specific symmetries.

Extends method for solving certain hydrodynamic systems.

Study symmetric linear bandits with hidden symmetry, achieving improved regret bounds.

Study finite group actions on aspherical manifolds, proving rigidity and symmetry bounds.

Proves Willmore conjecture for surfaces with specific symmetries.

Study proves radial symmetry of solutions to certain nonlinear equations in space forms.

Study of spacetimes in cosmology without symmetry assumptions.

Proves existence and trapped surface formation for Einstein-Vlasov system without symmetry assumptions.

New classification of conformal structures with maximal $G_2$ symmetry.

Paper proves trapped surface formation for EMCSF system without symmetry assumptions.

Classifies contravariant matrix-valued valuations on polytopes without continuity assumptions.

In this paper, it is shown that (with no additional assumptions) on a compact 7-dimensional manifold which admits a $G_2$-structure soliton solutions to the Laplacian flow of R. Bryant can only be shrinking or steady. We also show that the space of symmetries (vector fields that annihilate via the Lie derivative) of a …

Bayesian Empirical Bayes extends EB to complex structures using probabilistic symmetry.