Two families of curvature inhomogeneous manifolds with constant Ricci eigenvalues are constructed.
problem Constructing curvature inhomogeneous Riemannian manifolds with constant Ricci eigenvalues.
method Derived from Einstein warped products and Riemannian Schwarzschild--Tangherlini manifold.
result Admits local isometric immersions and isometric embeddings of minimum codimension.
We construct uncountably many isoparametric families of hypersurfaces in Damek-Ricci spaces. We characterize those of them that have constant principal curvatures by means of the new concept of generalized Kahler angle. It follows that, in general, these examples are inhomogeneous and have nonconstant principal curvatu…
The paper studies inhomogeneous isoparametric hypersurfaces in pseudo-spheres.
problem Investigating inhomogeneous isoparametric hypersurfaces in pseudo-sphere.
method Construction of Clifford systems and analysis of isoparametric hypersurfaces.
result Connected isoparametric hypersurfaces of OT-FKM-type in pseudo-spheres are inhomogeneous under specific conditions.
New examples of hypersurfaces found in quaternionic hyperbolic spaces.
problem Classifying actions on symmetric spaces of rank one.
method Cohomogeneity one actions and orbit equivalence.
result Uncountably many inhomogeneous isoparametric families of hypersurfaces.
Enhanced Bishop-Gromov theorem for homogeneous and inhomogeneous spaces.
problem Bounding the volume growth of geodesic balls in spaces.
method Introducing coefficient shuffling and using the Raychaudhuri equation, geodesic flow conservation, and the full spectrum of Ricci curvature.
result Upper bounds on the average rate of growth of geodesics for finite-volume inhomogeneous spaces.
Constructs solutions to Einstein-Maxwell-current system using Sasakian manifolds.
problem Solving the Einstein-Maxwell-Current system with inhomogeneous charged particle density.
method Using Sasakian manifolds to specify magnetic field and electric current.
result Solutions with arbitrary function describing charged particle density and curvature.
Study quantizes energy distribution in inhomogeneous phase transitions.
problem Quantifying energy distribution in inhomogeneous Allen-Cahn phase transitions.
method Analysis of varifolds and convergence of integer rectifiable varifolds.
result Equidistribution of energy between Dirichlet and Potential energy in phase field limit.
The paper studies how certain surfaces evolve in space without collapsing.
problem Evolution of surfaces with inhomogeneous speeds without collapsing.
method Analyzes curvature flows with a specific speed function and structural conditions.
result Establishes exterior noncollapsing estimates for the flow.
We show there are precisely 15 inhomogeneous biquotients of the form Sp(3)//Sp(1)2 and show that at least 8 of them admit metrics of quasi-positive curvature.
Survey shows deformations of homogeneous metrics in curvature homogeneous manifolds.
problem Understanding curvature homogeneous manifolds with nontrivial κ-nullity.
method Analyzes deformations of homogeneous metrics along submersions.
result Identifies two new examples of curvature homogeneous manifolds.
A coupling by reflection of a time-inhomogeneous diffusion process on a manifold are studied. The condition we assume is a natural time-inhomogeneous extension of lower Ricci curvature bounds. In particular, it includes the case of backward Ricci flow. As in time-homogeneous cases, our coupling provides a gradient esti…
Inhomogeneous plasmas filaments instabilities are investigated by using the techniques of classical differential geometry of curves where Frenet torsion and curvature describe completely the motion of curves. In our case the Frenet frame changes in time and also depends upon the other coordinates taking into account th…
The paper proves the existence of hypersurfaces with prescribed mean curvature.
problem Proving the existence of hypersurfaces with prescribed mean curvature.
method PDE theoretic approach using mountain pass construction and regularity results for integral varifolds.
result Existence of quasi-embedded, boundaryless hypersurfaces with prescribed mean curvature.
The Finsler spaces in which the tangent Riemannian spaces are conformally flat prove to be characterized by the condition that the indicatrix is a space of constant curvature. In such spaces the Finslerian normalized two-vector angle can be explicated from the respective two-vector angle of the associated Riemannian sp…
Study magnetic field evolution in inhomogeneous axion stars.
problem Magnetic field evolution in axion stars with spatial inhomogeneity.
method Derived new induction equation for magnetic field, analyzed CS waves interactions, and considered compact domain effects.
result Spatial inhomogeneity of pseudoscalar field significantly affects magnetic field evolution.
Study on harmonic functions in spaces with collapsing behaviors.
problem Harmonic functions on spaces with inhomogeneous collapsing behaviors at infinity.
method Analysis of complete and incomplete spaces with nonnegative Ricci curvature.
result Any nonconstant harmonic function yields a definite exponential growth rate.
Study shows deformations of quaternionic Kähler manifolds are locally inhomogeneous.
problem Understanding deformations of quaternionic Kähler manifolds.
method Proved one-loop deformation of quaternionic Kähler manifolds are locally inhomogeneous.
result Full isometry group of one-loop deformations has cohomogeneity one.
We introduce a new parameter to measure the inhomogeneity of training datasets.
problem The need for non-stationary models in supervised learning.
method We introduce a new parameter, the inhomogeneity parameter, to measure the inhomogeneity of training datasets.
result A training set with a non-zero inhomogeneity parameter requires a non-stationary model for accurate predictions.
Researchers describe a specific type of submanifolds in Euclidean space.
problem Understanding inhomogeneous almost symmetric submanifolds.
method Completely describing submanifolds as unions of parallel symmetric submanifolds.
result Described inhomogeneous properly embedded almost symmetric submanifolds as unions of symmetric submanifolds.
Sharp threshold found for Frechet mean of inhomogeneous graphs.
problem Finding the Frechet mean of inhomogeneous Erdos-Renyi random graphs.
method Thresholding the expected adjacency matrix of the ensemble.
result The Frechet mean graph of inhomogeneous Erdos-Renyi random graphs exhibits a sharp threshold.
We assign a measure to an upper semicontinuous function which is subharmonic with respect to the mean curvature operator, so that it agrees with the mean curvature of its graph when the function is smooth. We prove that the measure is weakly continuous with respect to almost everywhere convergence. We also establish a …
We construct examples of inhomogeneous isoparametric real hypersurfaces in complex hyperbolic spaces.
Develops time-inhomogeneous polynomial processes for better model calibration and seasonality capture.
problem Calibration to market prices and seasonality in term-structure models.
method Introduces time-inhomogeneous polynomial processes with time-dependent coefficients and characterizes them using semimartingale characteristics. Alternative numerical approximations using Magnus series are explored.
result Matrix exponentials are not sufficient for computing moments in time-inhomogeneous polynomial processes, necessitating alternative numerical methods.
Paper examines floating exercise boundaries for American options in time-inhomogeneous models.
problem Floating exercise boundaries in time-inhomogeneous models with negative interest rates or yields.
method Semi-analytical approach for pricing American options.
result Specialized pricing methodologies are required for models with floating exercise boundaries.
Efficiently matches random graphs with inhomogeneous edge probabilities.
problem Matching latent vertex correspondence between two correlated random graphs with inhomogeneous edge probabilities.
method Inspired by Ding et al. (2021), an efficient matching algorithm is developed with conditions on minimal average degree and minimal correlation.
result An efficient matching algorithm is obtained as long as the minimal average degree is at least Ω(log2n) and the minimal correlation is at least 1−O(log−2n). Unique inhomogeneous ruled hypersurface found in complex hyperbolic space.
problem Classifying ruled real hypersurfaces with constant norm.
method Analyzing nonflat complex space forms, proving existence and uniqueness.
result Existence of a unique inhomogeneous example in complex hyperbolic space.
We construct explicit global symplectic coordinates for the Calabi's inhomogeneous Kaehler-Einstein metric on tubular domains.
Study phase transitions with prescribed mean curvature in Riemannian manifolds.
problem Understanding phase transitions with prescribed mean curvature in geometric settings.
method Analyzing solutions to inhomogeneous semilinear elliptic PDEs, establishing bounds and asymptotics.
result Established upper and lower bounds for eigenvalues of phase transition problems.
New hypergraph clustering method assigns different costs to hyperedge cuts.
problem Hypergraph partitioning assumes uniform costs for different hyperedge cuts.
method Inhomogeneous hypergraph partitioning assigns different costs to different hyperedge cuts.
result Inhomogeneous partitioning offers significant performance improvements in various applications.
Study on droplet flow on uneven surfaces, proving existence and properties.
problem Understanding droplet movement on irregular surfaces.
method Existence of smooth flow and 1/2-Hölder continuous minimizing movement solutions.
result Properties of minimizing movements including comparison principles and uniform boundedness.
In this paper, we prove global second derivative estimates for solutions of the Dirichlet problem for the Monge-Ampere equation when the inhomogeneous term is only assumed to be Holder continuous. As a consequence of our approach, we also establish the existence and uniqueness of globally smooth solutions to the second…
Study optimal algorithms for recovering signals through inhomogeneous low-rank channels.
problem Recovering signals through an inhomogeneous low-rank matrix channel.
method Derive and analyze an approximate message-passing algorithm (AMP) and a spectral method.
result The AMP iteration matches the conjectured optimal computational phase transition.
In this note, we propose Bernstein's problem and De Giorgi's conjecture for spatially inhomogeneous equations, as well as De Giorgi's conjecture for system of reaction-diffusion equations.
An extension of the ambient metric construction of Fefferman-Graham to infinite order in even dimensions is described. The main ingredients are the introduction of "inhomogeneous ambient metrics" with asymptotic expansions involving the logarithm of a defining function homogeneous of degree 2, and an invariant procedur…
Unified method detects and localizes anomalous cliques in inhomogeneous networks.
problem Detect and localize anomalous cliques in inhomogeneous networks.
method Unified method based on egonets for detection and localization.
result Unified method can detect and localize anomalous cliques in inhomogeneous networks.
This paper generalizes Moody's correlated binomial default distribution for homogeneous (exchangeable) credit portfolio, which is introduced by Witt, to the case of inhomogeneous portfolios. As inhomogeneous portfolios, we consider two cases. In the first case, we treat a portfolio whose assets have uniform default cor…
Establishes exponential contraction in Wasserstein distance on manifolds and flows.
problem Analyzing contraction rates in Wasserstein distance on manifolds and their evolution.
method Explicit estimates and extension to evolving manifolds under geometric flow.
result Gradient estimates with exponential contraction rate under weak curvature conditions.
We consider a heat kernel approach for the development of stochastic pricing kernels. The kernels are constructed by positive propagators, which are driven by time-inhomogeneous Markov processes. We multiply such a propagator with a positive, time-dependent and decreasing weight function, and integrate the product over…
Optimal spectral method found for inhomogeneous spiked Wigner model.
problem Structured noise in learning scenarios.
method Random matrix theory and spectral analysis.
result Optimal threshold for phase transition in block-structured Wigner model.
We discuss several issues regarding material homogeneity and strain compatibility for materially uniform thin elastic shells from the viewpoint of a 3-dimensional theory, with small thickness, as well as a 2-dimensional Cosserat theory. A relationship between inhomogeneity and incompatibility measures under the two des…
This thesis is concerned with equidistant foliations of Euclidean space, i.e. partitions into complete, connected, properly embedded smooth submanifolds. The space of leaves is an Alexandrov space of nonnegative curvature and the canonical projection is a submetry. Generalizing a result of Gromoll and Walschap we show …
We construct new complete, compact, inhomogeneous Einstein metrics on S^{m+2} sphere bundles over 2n-dimensional Einstein-Kahler spaces K_{2n}, for all n \ge 1 and all m \ge 1. We also obtain complete, compact, inhomogeneous Einstein metrics on warped products of S^m with S^2 bundles over K_{2n}, for m>1. Additionally,…
Study volatility models with rough paths, focusing on large deviations and option behavior.
problem Analyzing volatility in financial markets with very rough paths.
method Introduced time-inhomogeneous stochastic volatility models with Volterra Gaussian processes.
result Obtained large deviation principles for log-price processes in super rough Gaussian models.
The paper constructs metrics with non-negative curvature and harmonic maps.
problem Constructing metrics with non-negative curvature and harmonic maps.
method Using Clifford systems and characteristic maps, the paper constructs metrics with non-negative curvature and harmonic representatives of certain elements in homotopy groups of spheres.
result The construction of a metric of non-negative curvature on S(η) which is diffeomorphic to the inhomogeneous focal submanifold M+ of OT-FKM type isoparametric hypersurfaces. New method constructs deformation groupoid for inhomogeneous pseudo-differential calculus.
problem Recovering inhomogeneous pseudo-differential calculus using a deformation groupoid.
method Elementary construction of deformation groupoid for Heisenberg calculus, then generalization to arbitrary filtrations.
result Elementary construction of deformation groupoid for inhomogeneous pseudo-differential calculus.
A new infinite series of Einstein metrics is constructed explicitly on S^2 x S^3, and the non-trivial S^3-bundle over S^2, containing infinite numbers of inhomogeneous ones. They appear as a certain limit of a nearly extreme 5-dimensional AdS Kerr black hole. In the special case, the metrics reduce to the homogeneous E…
We show how the relation between Poisson brackets and symplectic forms can be extended to the case of inhomogeneous multivector fields and inhomogeneous differential forms (or pseudodifferential forms). In particular we arrive at a notion which is a generalization of a symplectic structure and gives rise to higher Pois…
New adaptive clustering method detects local inhomogeneity.
problem Detecting clusters in data without specifying their structure.
method Adaptive Weights Clustering (AWC) method that grows locality parameter at each step.
result AWC method can recover clusters with sharp edges or manifold structure.