arXiv research

The paper extends holomorphic motions over non-simply connected Riemann surfaces.

We show that the graph of a holomorphic motion of the unit disc cannot be biholomorphic to a strongly pseudoconvex domain in C n .

Representations of coherent state Lie algebras on coherent state manifolds as first order differential operators are presented. The explicit expressions of the differential action of the generators of semisimple Lie groups determine for linear Hamiltonians in the generators of the groups first order differential equati…

We prove that a primitive harmonic map is equivariant if and only if it admits a holomorphic potential of degree one. We investigate when the equivariant harmonic map is periodic, and as an application discuss constant mean curvature cylinders with screw motion symmetries.

Given an irreducible unitary representation of a cocompact lattice of SL(2,C), we explicitly write down a solution of the Strominger system of equations. These solutions satisfy the equation of motion, and the underlying holomorphic vector bundles are stable.

The fact that minimal surfaces in the four-dimensional Euclidean space admit natural parameters implies that any minimal surface is determined uniquely up to a motion by two curvature functions, satisfying a system of two PDE's (the system of natural PDE's). In fact this solves the problem of Lund-Regge for minimal sur…

Hamilton flows on Kähler manifold for which all trajectories are $H$-planar curves (complex analog of geodesics) are considered. These flows are called $H$-planar. The equation which has to obey the Hamiltonian of $H$-planar Hamilton flow is received and the method of finding general solution of this equation is propos…

In 1974, Berezin proposed a quantum theory for dynamical systems having a Kähler manifold as their phase space. The system states were represented by holomorphic functions on the manifold. For any homogeneous Kähler manifold, the Lie algebra of its group of motions may be represented either by holomorphic differential …

We prove that a given Calabi-Yau threefold with a stable holomorphic vector bundle can be perturbed to a solution of the Strominger system provided that the second Chern class of the vector bundle is equal to the second Chern class of the tangent bundle. If the Calabi-Yau threefold has strict SU(3) holonomy then the eq…

Entire area-minimizing surfaces of density 2 are planar or quadratic

A minimal space-like surface in Minkowski space-time is said to be of general type if it is free of degenerate points. The fact that minimal space-like surfaces of general type in Minkowski space-time admit canonical parameters of the first (second) type implies that any minimal space-like surface is determined uniquel…

Inspired by Berndtsson's work on the subharmonicity property of the Bergman kernel, we give a local variation formula of the full Bergman kernels associated to deformations of complex manifolds. In compact case, it follows from the reproducing property of the Bergman kernel and the curvature formula of the 0-th direct …

The jet formalism for Classical Field theories is extended to the setting of Lie algebroids. We define the analog of the concept of jet of a section of a bundle and we study some of the geometric structures of the jet manifold. When a Lagrangian function is given, we find the equations of motion in terms of a Cartan fo…

Deformed holomorphic Chern-Simons theory yields new instantons.

Revisits superfields and geometry, offering new formulations and interpretations.

The paper provides a Weierstrass representation for maximal space-like surfaces in 4D pseudo-Euclidean space.

Classifies 6D homogeneous spaces with holomorphically trivial canonical bundle.

Skew parallelogram nets factorize, encompassing discrete differential geometry.

Let (ρ_\la)_{\la\in \La} be a holomorphic family of representations of a surface group π_1(S) into PSL(2,C), where S is a topological (possibly punctured) surface with negative Euler characteristic. Given a structure of Riemann surface of finite type on S we construct a bifurcation current on the parameter space \La, t…

I use local differential geometric techniques to prove that the algebraic cycles in certain extremal homology classes in Hermitian symmetric spaces are either rigid (i.e., deformable only by ambient motions) or quasi-rigid (roughly speaking, foliated by rigid subvarieties in a nontrivial way). These rigidity results ha…

MT-VAE learns motion transitions for generating diverse future motions.

Introduces Motion Programs for better video analysis of human motion.

We study a particular class of supersymmetric M-theory eight-dimensional non-geometric compactification backgrounds to three-dimensional Minkowski space-time, proving that the global space of the non-geometric compactification is still a differentiable manifold, although with very different geometric and topological pr…

Study motion planning for points avoiding obstacles in a plane.

Paper introduces new motion synthesis model using normalizing flows.

Programmatic Motion Concepts learn human actions from paired videos.

Unified framework for human motion generation on Riemannian manifolds.

Study on determinants of unitary Brownian motion and their asymptotic laws.

New framework predicts diverse, contextually plausible 3D human motions.

Formula calculates optimal number of paths for correlated Brownian motions.

Neural network predicts vessel motions with high accuracy.

Study refracted skew Brownian motion, find densities and asymptotics.

Study fractal dimension for motion without crossing a subset.

Neural network estimates rigid motion in stroke imaging to improve image quality.

Study cohomological equation for robotic screw motions on SE(3).

New approach for obstacle avoidance in robotics using learned representations.

The paper presents a method to reduce arm motion complexity for prosthetics and robotics.

Paper defines multi-dimensional fractional Brownian motion under volatility uncertainty.

Paper introduces a new method for generating diverse human motion predictions.

Researchers calculate the Laplace transform of a geometric Brownian motion integral.

Researchers created a continuous Markov martingale that mimics Brownian motion but lacks the strong Markov property.

We consider $n$-dimensional discrete motions such that any two neighbouring positions correspond in a pure rotation ("rotating motions"). In the Study quadric model of Euclidean displacements these motions correspond to quadrilateral nets with edges contained in the Study quadric ("rotation nets"). The main focus of ou…

Improved vehicle motion prediction with uncertainty estimation.

A framework for computing holonomy groups of hybrid systems to achieve forward motion.

The paper explores representations of graph manifolds to Seifert motion groups.

Geodesic walks converge to Brownian motion on Finsler manifolds.

MPNet uses neural networks for efficient motion planning.

Study homotopy motions of surfaces in 3-manifolds.