A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
We establish a new symmetrization procedure for the isoperimetric problem in symmetric spaces of noncompact type. This symmetrization generalizes the well known Steiner symmetrization in euclidean space. In contrast to the classical construction the symmetrized domain is obtained by solving a nonlinear elliptic equatio…
Paper introduces capillary Schwarz symmetrization in half-space.
Study finds lower bounds for energy on fibred manifolds using fiberwise symmetrization.
Developed a new symmetric hyperbolic formulation for Einstein-Yang-Mills system.
The paper verifies a conjecture about the index of symmetric spaces.
Proves gap rigidity theorem for Hermitian symmetric spaces.
Paper proves March's criterion for transience on symmetric manifolds.
Finite index solutions to Bernoulli problem are always axially symmetric.
Paper finds smooth convex solutions to curvature problem.
Symmetric TSP is structurally equivalent to a constrained Group Steiner Tree Problem.
Eisermann and Lamm introduced a notion of symmetric equivalence among symmetric union diagrams and studied it using a refined form of the Jones polynomial. We introduced invariants of symmetric equivalence via refined versions of topological spin models and provided a partial answer to a question left open by Eisermann…
Having developed a description of indefinite extrinsic symmetric spaces by corresponding infinitesimal objects in the preceding paper we now study the classification problem for these algebraic objects. In most cases the transvection group of an indefinite extrinsic symmetric space is not semisimple, which makes the cl…
Proves stability of Einstein metrics on specific symmetric spaces.
Riemannian symmetric spaces are fundamental objects in finite dimensional differential geometry. An important problem is the construction of symmetric spaces for generalizations of simple Lie groups, especially their closest infinite dimensional analogues known as Kac-Moody groups. We solve this problem and construct a…
We consider the problem of learning regression functions from pairwise data when there exists prior knowledge that the relation to be learned is symmetric or anti-symmetric. Such prior knowledge is commonly enforced by symmetrizing or anti-symmetrizing pairwise kernel functions. Through spectral analysis, we show that …
Study proves inequalities for eigenvalues of symmetric domains in space forms.
The paper characterizes spherically symmetric metrics with scalar curvature.
Machine learning models solve inverse eigenvalue problems for symmetric potentials and refractive indices.
Cohomogeneity-one actions on symmetric spaces of mixed type
New inequality shows energy growth and decay in geometric problems.
Sym-NCO leverages symmetricities to improve DRL-NCO performance.
The paper classifies Landsberg spherically symmetric Finsler metrics in various dimensions.
We consider a class of overdetermined problems in rotationally symmetric spaces, which reduce to the classical Serrin's overdetermined problem in the case of the Euclidean space. We prove some general integral identities for rotationally symmetric spaces which imply a rigidity result in the case of the round sphere.
This paper investigates symmetric ribbon numbers of low-complexity knots.
Riemannian and pseudo-Riemannian symmetric spaces with semisimple transvection group are known and classified for a long time. Contrary to that the description of pseudo-Riemannian symmetric spaces with non-semisimple transvection group is an open problem. In the last years some progress on this problem was achieved. I…
In this paper, we address the problem of determining a function in terms of its orbital integrals on Lorentzian symmetric spaces. It has been solved by S. Helgason for even-dimensional isotropic Lorentzian symmetric spaces via a limit formula involving the Laplace-Beltrami operator. The result has been extended by J. O…
We investigate existence and stability of rotationally symmetric critical immersions of variational problems of higher order which were considered by Nitsche.
There is a well developed theory of weakly symmetric Riemannian manifolds. Here it is shown that several results in the Riemannian case are also valid for weakly symmetric pseudo-Riemannian manifolds, but some require additional hypotheses. The topics discussed are homogeneity, geodesic completeness, the geodesic orbit…
We study the problem of conformally deforming a metric to a prescribed symmetric function of the eigenvalues of the Ricci tensor. We prove an existence theorem for a wide class of symmetric functions on manifolds with positive Ricci curvature, provided the conformal class admits an admissible metric.
This is a survey on known results and open problems about Smooth and PL-Rigidity Problem for negatively curved locally symmetric spaces. We also review some developments about studying the basic topological properties of the space of negatively curved Riemannian metrics and the Teichmuller space of negatively curved me…
New deep learning methods solve symmetric PDEs efficiently.
Study of symmetric unions of knots with new inequality and epimorphism results.
Solves Christoffel-Minkowski problem for axially symmetric bodies.
The strong symmetric genus of a finite group is the minimum genus of a compact Riemann surface on which the group acts as a group of automorphisms preserving orientation. A characterization of the infinite number of groups with strong symmetric genus zero and one is well-known and the problem is finite for each strong …
The paper classifies spherically symmetric sprays and their curvature properties.
Motivated by the study of ribbon knots we explore symmetric unions, a beautiful construction introduced by Kinoshita and Terasaka 50 years ago. It is easy to see that every symmetric union represents a ribbon knot, but the converse is still an open problem. Besides existence it is natural to consider the question of un…
We present another proof of the sharp inequality for Paneitz operator on the standard three sphere, in the spirit of subcritical approximation for the classical Yamabe problem. To solve the perturbed problem, we use a symmetrization process which only works for extremal functions. This gives a new example of symmetriza…
Study of 4D symmetric spaces with (2,2) signature.
The article contains a survey of results on length-commensurable and isospectral locally symmetric spaces and related problems in the theory of semi-simple algebraic groups.
New method for mixed memberships using symmetrized Laplacian inverse matrix.
Paper finds obstructions to compact Clifford-Klein forms for tangential symmetric spaces.
In this paper we address the problem of studying those Kähler manifolds whose first two coefficients of the associated TYZ expansion vanish and we prove that for a locally Hermitian symmetric space this happens only in the flat case. We also prove that there exist nonflat locally Hermitian symmetric spaces where all th…
Study on deformations of symmetric spaces using Jordan algebras.
The paper proves that symmetric sets with minimal Gaussian surface area are nearly convex cylinders.
Symmetric CNNs improve sequential recommendation and protein structure prediction.
Characterizes spherical Finsler metrics satisfying a specific condition.
This paper is motivated by the real symplectic isotopy problem : does there exists a nonsingular real pseudoholomorphic curve not isotopic in the projective plane to any real algebraic curve of the same degree? Here, we focus our study on symmetric real curves on the projective plane. We give a classification of real s…
We prove the existence and uniqueness of the Dirichlet problem for spacelike, spherically symmetric, constant mean curvature equation with symmetric boundary data in the extended Schwarzschild spacetime. As an application, we completely solve the CMC foliation conjecture which is posted by Malec and O Murchadha in 2003…