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


208 публикаций

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Heavenly equations in de Sitter space
Generalized Chen's inequalities for Riemannian submersions and Riemannian maps with Applications
Bottom of the spectrum of complete noncompact Kähler manifolds
Linear Hamiltonians in generators of the real Jacobi group on the extended Siegel-Jacobi space and equations of motion attached
A Positive Mass Theorem for Continuous Metrics
The alignment time function
Approximation and interactive design with exact 3D elastic curves
Positive Scalar Curvature Obstructions via Singular Dimension Descent
The Token Is a Group Element: On Lie-Algebra Attention over Matrix Lie Groups
Gromov's Euclidean Endpoint $C^0$ Rigidity for the Positive Mass Theorem
Quadratic one-forms on logarithmic Higgs moduli
Holomorphic tensors on products of algebraic cones
On the bisections of a local Lie grpoupod
Diffeomorphic Logarithm of Special Orthogonal Matrices
Cohomogeneity one actions on symmetric spaces of mixed type
Sobolev and Michael-Simon inequalities via the ABP method beyond Euclidean volume growth
The volume of tubes in Lie groups
Total curvature and length estimates for timelike curves in Lorentzian length spaces
Potential functions in information geometry via bi-forms
Balancing The 2-Systoles Of Some K{ä}hler Manifolds With Positive Scalar Curvature
Ricci solitons as critical points of quadratic curvature functionals
Entire area-minimizing surfaces in $\mathbf{R}^n$ of density two are quadratic or planar
Kähler-Ricci Flow: from divisors to cusps
Admissibility, Topology, and the $σ_k$-Loewner--Nirenberg problem
Intermediate Pseudoconvexity of Fiber Bundles
Geometry of non-Hermitian Yang--Mills moduli spaces
The Cone Projection $f(z)=\dfrac{z}{1+|z|/R}$ Geometric structure and the Self-Directrix Theorem
Existence of twisted Hermitian-Einstein metrics on unstable vector bundles
Gromov's Euclidean Endpoint $C^0$ Rigidity for the Positive Mass Theorem
Rigidity Theorems for the Weyl Problem of Convex Surfaces in Hyperbolic 3-Space
Quantitative flatness and obstructions in Fourier analysis
The Sesquiharmonic Map Flow from Riemannian Surfaces
Gromov-Hausdorff convergence of time-slices of singular Ricci flows in dimension three
Sharp stability of Alexandrov's theorem for $C^1$ domains in the small-excess regime
Sub-Riemannian Selberg Trace Formulae for Compact Quotients of SL(2,R) and Determinants of Sub-Laplacians
A singularity theorem in terms of asymptotic expansion
Continuum-wise hyperbolicity is exactly the pseudo-Anosov dynamics with spine singularities
Scalar curvature, sharp bottom spectrum and geometric rigidity
Long-time existence of some geometric flows with bounded scalar curvature
Effective Angular Asymptotics and the Sharp $D^{-3}$ Horoconvex Gap Scale
Ricci solitons from the perspectives of energy function
Gaussian-Weighted Curvature Gaps for Self-Shrinkers
Holomorphic families of knots
Quasilinear Liouville equation on manifolds with nonnegative Ricci curvature
Hypersurfaces with Constant Ricci Eigenvalues in Real Space Forms
A Levi-type decomposition on two-step solvable Lie algebras with a complex structure
Kähler Hyperbolicity Modulus for Simply-connected Kähler Hyperbolic manifolds
Наследие Вагнера. К 90-летию кафедры геометрии Саратовского государственного университета
Optimal geometric estimates for compact Kähler manifolds of a Nash entropy bound
A non-trivial index difference on surfaces of genus at least $3$
A Local Singularity Analysis for the Ricci Flow and its Applications to Ricci Flows with Bounded Scalar Curvature -- Part II
On the structure of complete $G_2$-solitons
The Morse index of constant curvature 2-spheres
Orbifold Uniformization of Complex Algebraic Variety by Stable Parabolic Higgs Bundle
Frenet turns
A Restricted Chen-Nagano Variational Principle for the Einstein-Hilbert Functional
Beltrami problem in dimension two: local normal forms
Generalizing Lusztig's total positivity II : geometric properties
Magnetic Brunn-Minkowski inequalities
On Brezis Open Problem 3.1
The Ollivier Ricci flow with prescribed curvature on infinite graphs
The Chern-Simons action for perturbed Dirac triples
Semistability and asymptotics of geometric flows
Jet Bundles as Higher-Order Polarised $k$-Contact Manifolds
Spherically symmetric, asymptotically flat Berwald vacuum solutions in Finsler gravity
Curvature of hyperbolic complex manifolds
Doubly warped product Einstein metrics on spheres
Variational Inverse Problems for Second Order ODEs with and without Constraints
Harmonic extension of Weil-Petersson circle homeomorphisms
Sasakian manifolds and spin-c Killing spinors
Nonparametric Riemannian Empirical Bayes, and Denoising Measurements on Manifolds
Solutions to Mean Curvature Flow with Uniform Bounds on the Mean Curvature and Its Gradient
The Dirichlet problem for the prescribed scalar curvature in Anti-de Sitter space
Spacetime Bartnik Mass Positivity and Temporal Monotonicity for Black Holes
Diffeologies on Locally Convex Spaces and Smooth Multiplication of Distributions
Optimal spectral rigidity of the hypercube via Bakry--Émery curvature
Distance, Normals and Double Normals for Real Plane Curves with Singularrities
Monotone quantities on $3$-manifolds with nonnegative scalar curvature
Conformal product structures on $S^3$
Near Isospectrality and Spectral Rigidity for Compact Locally Symmetric Manifolds
Quantization of measures in Carnot groups
Special structures on almost abelian solvmanifolds
Normal curvature bounds for immersions into Riemannian domains
Positive resolution of Bartnik's cosmological splitting conjecture
Cylindrical generalized Ricci solitons in three dimensions
Mean curvature and closed geodesics in convex hypersurfaces
Special Lagrangian submanifolds and circle collapse on K3
A note on the pluriclosed flow on balanced manifolds with $c_1=0$
On the integrability of generalized almost complex structures on $\mathbb{S}^6$
Third order Einstein deformations for Kaehler-Einstein metrics
Curvature of Lie Groupoids with Source-Fibre Metric and Riemannian Lie Algebroids
Shapes of light: singularities of slant functions and the Gauss map of a surface
Betti and Hodge numbers of solvmanifolds arising from integer polynomials
Doubly Totally-Umbilical Statistical Submanifolds in the Probability Simplex
Analytic patch trees: branch interface inheritance and fractal dimension fields
Second-Jet Equivariant $η$ Separations on Lens Spaces
Mean convex flows with surgery
On coKähler structures on Lie algebra
Ollivier-Ricci Curvature for Causal Sets
Local description of gl-regular Haantjes operators
Holomorphic polynomial crystallographic actions of nilpotent groups
A Dynkin condition for manifolds with boundary
K-semistability and singularities of normal affine cones
Shi-type estimates and finite-time singularities of reasonable flows of Spin(7)-structures
Constant mean curvature surfaces in the sub-Lorentzian Heisenberg group
Mixed Killing Vector Fields on Cigar Ricci-Bourguignon Solitons
Timelike meridian surfaces of hyperbolic type in the Minkowski 4-space
Inequivalence of the various notions of completeness for Cartan geometries
On a Local Radial Rigidity Phenomenon of Elliptic Systems on Riemannian Manifolds
Weyl-type theorems in Galilei and Carroll geometry
Weak almost contact structure with B-metric
Stable Degeneration, Non-degenerate Forms, and Kaledin's Conjecture
Timelike ideal boundary of non-positively curved Lorentzian spaces
Stochastic completeness for landmark space
About top-degree $L^2$- and $L^{2,\mathrm{loc}}$-Dolbeault cohomologies of complex spaces with pseudoconvex boundary
A family of parametric isoperimetric-type inequalities with multiple geometric quantities
Cohomogeneity-one Einstein metrics on closed $4$-manifolds
Integrability of Lawson-Osserman Cone and its Applications
Lie's classification of finite dimensional algebras of Vector Fields in C^N
Scalar Curvature Compactness for Warped Products on $\mathbb{S}^2\times\mathbb{S}^1$ with Varying Base Metrics
Invariantised Euler-Lagrange equations and conserved quantities for nonconservative Herglotz variational problems
The Cartan-Kähler theorem for exterior differential systems on transitive Lie algebroids
Shifted lagrangian structures in Poisson geometry
Weak solutions of the generalized Monge-Ampère equation and the supercritical deformed Hermitian-Yang-Mills equation: boundary cases
A solution to the Yau-Tian-Donaldson Conjecture through Special Fujita Approximations
Lower bounds for the low Steklov eigenvalues
Invariant statistical connections on the multivariate centered Gaussian model and their moduli spaces
Free Boundary Plateau Model Cones in $\mathbb{B}^n$ are Rigid under Conformal Minimal Immersions
Super integrable hierarchies associated with color Lie algebra
Artificial Intelligence and the Autonomization of Mathematics
Conjugate radius of open manifolds
$G_2$ and the Maximally Symmetric (3, 8) Distribution with 6-Dimensional Square
The Fujimoto Conjecture via Total Positivity
Unbounded Topology of Nodal Sets of Harmonic Functions
Generalized Minkowski Theorem for Tetrahedra in ${\rm dS}^3$ and ${\rm AdS}^3$
Stability of the Injectivity Radius and the Cut Locus of Submanifolds under Perturbations
Total curvature of a complete minimal surface and the modified defect relation of a Fermat hypersurface for the Gauss map
Generalization of Newton's minimal resistance problem to Riemannian surfaces
The Wasserstein--Ebin Metric: A Geometric Lift of Unbalanced Optimal Transport to the space of Riemannian metrics
Practical tensor calculus on embedded submanifolds of arbitrary codimension
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