arXiv research

Study on special anisotropic conformal changes of conic pseudo-Finsler surfaces.

The paper studies anisotropic conformal changes in pseudo-Finsler surfaces.

This research examines anisotropic conformal transformations of pseudo-Finsler surfaces.

We formulate the theory of nearly autoparallel maps (generalizing conformal transforms) of locally anisotropic spaces and define the nearly autoparallel integration as the inverse operation to both covariant derivation and deformation of connections by nearly autoparallel maps. By using this geometric formalism we cons…

We consider the anisotropic Calderon problem of recovering a conductivity matrix or a Riemannian metric from electrical boundary measurements in three and higher dimensions. In the earlier work \cite{DKSaU}, it was shown that a metric in a fixed conformal class is uniquely determined by boundary measurements under two …

New Kelvin transform for anisotropic elliptic problems.

We generalize Penrose's notion of conformal infinity of spacetime, to situations with anisotropic scaling. This is relevant not only for Lifshitz-type anisotropic gravity models, but also in standard general relativity and string theory, for spacetimes exhibiting a natural asymptotic anisotropy. Examples include the Li…

Paper proves geodesics and focal points unchanged by conformal changes in pseudo-Finsler manifolds.

We present a geometric approach to the field theory with higher order anisotropic interactions. The concepts of higher order space, or locally anisotropic, space (in brief, h-space, or la-space) are introduced as general ones for various types of higher order extensions of Lagrange and Finsler geometry and higher dimen…

The horizon and geodesic structure of static configurations generated by anisotropic conformal transforms of the Schwarzschild metric is analyzed. We construct the maximal analytic extension of such off--diagonal vacuum metrics and conclude that for small deformations there are different classes of vacuum solutions of …

Study anisotropic obstacle problem for minimal surfaces using Cahn-Hoffman transform.

We review the geometric setting of the field theory with locally anisotropic interactions. The concept of locally anisotropic space is introduced as a general one for various type of extensions of Lagrange and Finsler geometry and higher dimension (Kaluza--Klein type) spaces. The problem of definition of spinors on gen…

Researchers solve an inverse problem for a semilinear elliptic equation on complex manifolds.

An introduction into the theory of locally anisotropic spaces (modelled as vector bundles provided with compatible nonlinear and distinguished linear connections and metric structures and containing as particular cases different types of Kaluza--Klein and/or extensions of Lagrange and Finsler spaces) is presented. The …

We show that holographic renormalization of relativistic gravity in asymptotically Lifshitz spacetimes naturally reproduces the structure of gravity with anisotropic scaling: The holographic counterterms induced near anisotropic infinity take the form of the action for gravity at a Lifshitz point, with the appropriate …

Study on Gauss map of anisotropic minimal surfaces with Morse index estimates.

Anisotropic obstacle problems and Stefan problem studied with evolving surfaces.

In this article we study the linearized anisotropic Calderon problem. In a compact manifold with boundary, this problem amounts to showing that products of harmonic functions form a complete set. Assuming that the manifold is transversally anisotropic, we show that the boundary measurements determine an FBI type transf…

In this article we consider the anisotropic Calderon problem and related inverse problems. The approach is based on limiting Carleman weights, introduced in Kenig-Sjoestrand-Uhlmann (Ann. of Math. 2007) in the Euclidean case. We characterize those Riemannian manifolds which admit limiting Carleman weights, and give a c…

We consider the mixed ray transform of tensor fields on a three-dimensional compact simple Riemannian manifold with boundary. We prove the injectivity of the transform, up to natural obstructions, and establish stability estimates for the normal operator on generic three dimensional simple manifold in the case of 1+1 a…

The Stone-Weierstrass theorem aids in solving inverse problems on specific manifolds.

Study on determining metrics via Dirichlet-to-Neumann map for harmonic maps.

Transformers handle infinite dimensional inputs effectively by feature extraction and dynamic feature selection.

Paper introduces capillary Schwarz symmetrization in half-space.

After giving a general introduction to the main known results on the anisotropic Calder{ó}n problem on n-dimensional compact Riemannian manifolds with boundary, we give a motivated review of some recent non-uniqueness results obtained in [5, 6] for the anisotropic Calder{ó}n problem at fixed frequency, in dimension n $…

New compact examples of pseudo-Kähler manifolds with essential conformal transformations found.

In this paper we consider the problem of identifying a connection $\nabla$ on a vector bundle up to gauge equivalence from the Dirichlet-to-Neumann map of the connection Laplacian $\nabla^*\nabla$ over conformally transversally anisotropic (CTA) manifolds. This was proved in \cite{LCW} for line bundles in the case of t…

The paper explores Finsler-type objects and their variational problems on spacetimes.

Study on conformal transformations of Cahen-Wallach spaces, focusing on fixed points and discontinuous groups.

Classifies conformal transformations in spacetimes without observer horizons.

Yau's Affine Normal Descent optimizes smooth unconstrained problems with geometrically adapted directions.

For a complete Riemannian metric, a pointwise conformal transformation may lead to a complete or incomplete transformed Riemannian metric, depending on the behavior of the conformal factor. We establish conditions on the growth of the conformal factor towards the infinity of the Riemannian metric, such that the conform…

In this paper, we investigate a holonomy invariant elliptic anisotropic surface energy for hypersurfaces in a complete Riemannian manifold, where "holonomy invariant" means that the elliptic parametric Lagrangian (i.e., a Finsler metric) of the Riemannian manifold used to define the anisotropic surface energy is consta…

Improved text classification performance through conformal transformations of kernels.

Paper proves anisotropic Minkowski inequality and related inequalities.

Study of Lorentzian manifolds with specific transformations.

The classical Liouville Theorem on conformal transformations determines local conformal transformations on the Euclidean space of dimension $\geq 3$. Its natural adaptation to the general framework of Riemannian structures is the 2-rigidity of conformal transformations, that is such a transformation is fully determined…

A new characterization of conformal transformations is given. By use of this, the general form of conformal transformation on two-dimensional Minkowski space is given and its conformal structure is analyzed.

A fast method learns plasma collision kernels from simulations, improving kinetic models.

Paper solves anisotropic capillary Minkowski problem for p ≥ 1.

Compact Finslerian manifolds don't admit non-trivial circle-preserving transformations.

Classifies 1-connected Lorentzian manifolds with essential conformal groups.

We study several problems concerning conformal transformation on metric measure spaces, including the Sobolev space, the differential structure and the curvature-dimension condition under conformal transformations. This is the first result about preservation of lower curvature bounds under perturbation, which is new ev…

ST-BCP narrows the coverage gap in BCP by transforming nonconformity scores.

Classification of Finslerian spaces with nontrivial concircular transformations.

Paper proves rigidity results for anisotropic capillary hypersurfaces.

Paper solves Minkowski problem for anisotropic p-torsional rigidity.

Anisotropic min-max theory constructs stable minimal surfaces in 3-manifolds.