Гладкие кривые и поверхности, кривизна, дифференциальные операторы и их геометрические приложения.


68 публикаций

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Riemannian Archetypal Analysis: Interpretable non-linear data analysis on deformed star distributions
Associative Structures in Pseudo-Riemannian Lie Algebras
Geometry of Neighborhoods of Minimal Rational Curves
A Local Minimizing Property of Strictly Stable Free Boundary Minimal Hypersurfaces
Spectral Properties of the Chen-Nagano Gauge on Einstein Manifolds
Existence, Stability, and Geometric Implications of $\ast$-$η$-Schouten Solitons on Kenmotsu Manifolds
$G_2$ and the Maximally Symmetric (3, 8) Distribution with 6-Dimensional Square
Empirical Hodge Laplacians, Cohomology Ring, and Manifold Learning
Extrinsic characterizations of biconservative surfaces in the $4$-dimensional hyperbolic space
The nearby Lagrangian conjecture for pinwheels
Refocusing spacetimes need not be strongly refocusing
Global exponential stability for the three-dimensional Navier-Stokes equations on hyperbolic space
Parallel Surfaces of Cuspidal Cross Caps
Stokes' theorem on positively graded groups
Linear quadratic optimal transport and interpolation inequalities
Geometrisation of 3-manifolds
Minimal dimension equivariant embeddings of real and complex flag manifolds into Euclidean spaces
Scalar curvature of self-shrinkers
Nested nodal loops for sums of Laplace eigenfunctions
The spacetime Penrose inequality under a quasi final state hypothesis
Existence of multi-monopoles on mapping tori
Classifying Slice-Regular Polynomials via Group Actions on the Twistor Space
Complex spinorial forms, Brinkmann four-manifolds, and self-dual bundle gerbes
Regularity of stable capillary minimal hypersurfaces
Complete gradient Ricci solitons with zero radial Weyl curvature
Anisotropic calibrations, adiabatic limits and mirror symmetry
Sharp Gaussian Isoperimetry along a Ricci Flow
Infinitesimal automorphisms and obstruction theory on the moduli of $L$-valued $G$-Higgs bundles
On the Lie Foliation structure of Walker Manifolds
Linear representations of manifolds
Berezin-Toeplitz Quantization of non-compact manifolds
Weak cosmic censorship for the circularly symmetric Einstein-scalar field system in $2+1$ dimensions
Minimal Hypersurfaces with constant scalar curvature in $\mathbf{S}^6$
О конформно киллинговых векторных полях на пятимерном 2-симметрическом неразложимом лоренцевом многообразии с тривиальным тензором Вейля
Инновационный метод определения параметров закруглений лесных автомобильных дорог
Стохастическая дифференциальная геометрия гладких поверхностей положительной кривизны
Общее невырожденное решение одной системы функциональных уравнений
Automorphisms of Lie groupoids and symplectic reduction on orbifolds
Terminal Hölder Closure in Curvature Estimates and its Application
Boundary Behavior of Bisectional Curvatures for Weighted Bergman Metrics
$κ$-solutions with the round cylinder as an asymptotic shrinker
Spectral splitting theorem and ends of minimal hypersurfaces
On the Ricci symmetries of a Kähler manifold
Minimal submanifolds confined in space
A min-max gap characterization of minimal foliations on the torus
A Guide to Applications of $k$-Contact Geometry in Dissipative Field Equations
Analytic local resolution of Medvedev's Morse index conjecture for the critical hyperbolic catenoid in $\mathbb{H}^3$
The $r^\sharp$ invariant as a discriminant for the survival of the H-flux under T-duality on product manifolds
Improvement of flatness in annuli
Steerable Neural ODEs on Homogeneous Spaces
Contact Whirl Curves in Sasakian Lorentzian 3-Manifolds
Explicit Laplace Spectra of Homogeneous Principal Bundles
The Geometric Wall: Manifold Structure Predicts Layerwise Sparse Autoencoder Scaling Laws
Minimal homogeneous submanifolds of complex hyperbolic spaces
Prescribing geodesics and a variational problem for Riemannian metrics
Infinitesimal Rigidity of Cyclic Surfaces and Alternating Surfaces
Structure of Torus Fibration Under the First Betti Number Restriction
The Newton's problem assuming non-constant density of the fluid
Circles-foliated stationary surfaces of the Dirichlet energy
Homothetical surfaces with constant mean curvature in hyperbolic space
Forman--Ricci Curvature on Contact-Sequence Temporal Networks via Spatiotemporal Prism Complexes
On the triviality of the generalized tangent bundle
Area of Hölder curves and coarea formula on the Heisenberg group
Discrete Mixed Quantization
The Shortest Geodesic Flower on a Manifold with Locally Convex Ends and Finite Volume
Complex methods in the asymptotics of Möbius energy integrals of helix curves
A necessary condition for cylindrical curves in terms of curvature and torsion
Geometric aspects of the curve shortening flow in the hyperbolic plane