Solves partial data Calderón problem on Riemann surfaces.
problem Calderón problem with partial data on Riemann surfaces.
method Reflection principle applied to connection Laplacian.
result Solves partial data Calderón problem.
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48 results for “connection principle”
Softens classical theorems on Ricci curvature.
problem Classical theorems on Ricci curvature with strict hypotheses.
method Soft, quantitatively optimal extensions in -topology.
result Optimal extensions to Ricci curvature theorems.
Proves bijection between smooth conformal immersions and immersions.
problem Finding conformal immersions of closed Riemannian surfaces.
method Reformulated using -principle and proved bijection on path connected components.
result Induces a bijection between smooth conformal immersions and immersions.
UMAP connects to Information Geometry principles.
problem None explicitly stated; focuses on connections.
method None explicitly stated; focuses on connections.
result UMAP has a natural geometric interpretation.
The duality principle connects algebraic curvature tensors in pseudo-Euclidean spaces.
problem Understanding algebraic curvature tensors in pseudo-Euclidean spaces.
method Proving equivalence between the Jordan-Osserman condition and the Rakić duality principle.
result The Osserman condition and the duality principle are equivalent in the diagonalisable case.
We investigate the validity of the equivalence principle along paths in gravitational theories based on derivations of the tensor algebra over a differentiable manifold. We prove the existence of local bases, called normal, in which the components of the derivations vanish along arbitrary paths. All such bases are expl…
General Relativity can be reformulated as a diffeomorphism invariant SU(2) gauge theory. A new action principle for this "pure connection" formulation of GR is described.
Extends variational principle to tensor Banach spaces.
problem High-dimensional partial differential equations and minimization problems.
method Describes tensor product as disjoint connected components, each modeled as a Banach manifold.
result Extension of Dirac-Frenkel variational principle to topological tensor spaces.
A conjecture about rational curves' formal principle and convergence proved for Goursat type families.
problem Formal principle and convergence for rational curves of Goursat type.
method Natural ODEs and Cartan connections constructed by Doubrov-Komrakov-Morimoto.
result The conjecture is proved for rational curves of Goursat type.
We embed KKT points in neural networks of different sizes.
problem Classifying data using homogeneous neural networks.
method Introducing KKT point embedding principle and proving it for different network types.
result KKT points of a smaller network can be mapped to those of a larger network via linear transformations.
Internal Lagrangians derived from variational principles.
problem Reproducing the principle of stationary action in variational geometry.
method Introducing stationary points of internal Lagrangians, establishing connections with symmetries and conservation laws, and investigating relations between non-degenerate and internal Lagrangians.
result Noether's theorem reformulated in terms of internal Lagrangians.
Thom announced a homological h-principle, which was later proven by connecting combinatorial techniques with Thurston's jiggling method.
problem The h-principle in immersion theory, particularly the sphere inside-out problem.
method Combining combinatorial techniques with Thurston's jiggling method.
result The announced homological h-principle was proven true.
A variational principle connects fields to principal bundles and Einstein-Yang-Mills systems.
problem Constructing variational problems on fields related to principal bundles and Einstein-Yang-Mills systems.
method Constructing a variational problem on fields defined on a manifold, leading to spontaneous symmetry breaking and identification with principal bundles.
result Global solutions of Euler-Lagrange equations lead to principal bundles and Einstein-Yang-Mills systems with a cosmological constant.
Paper presents an action principle for Einstein-Weyl equations in 3D.
problem Finding an action principle for Einstein-Weyl equations.
method Metric affine f(R) gravity action plus additional terms involving Lagrange multipliers and gravitational Chern-Simons contributions.
result The Weyl vector dynamics is governed by a special case of the generalized monopole equation.
Reduces constructing multiplicative connections to simpler tasks.
problem Constructing multiplicative connections on proper Lie groupoids.
method Reduction to simpler tasks involving proper and regular Lie groupoids.
result Simpler methods for constructing multiplicative connections.
Study of complex Hessian equations using subharmonic functions and geodesics.
problem Understanding geodesics within complex Hessian equations.
method Perron envelope construction, comparison principle, rooftop equality, Kiselman minimum principle.
result Established criterion for geodesic connectivity among -subharmonic functions.
Simple connection between Harnack inequalities and concavity of arrival time functions.
problem Proving differential Harnack inequalities for various flows.
method Directly proving concavity properties of time-of-arrival functions for a class of flows using a concavity maximum principle.
result Short proof of Hamilton's and Andrews' differential Harnack inequalities.
New balanced metrics introduced for SPD matrices, improving metric choice.
problem Lack of principles for choosing SPD matrix metrics.
method Introducing balanced metrics that relate existing metrics.
result Two new balanced metric families introduced: mixed-power-Euclidean and mixed-power-affine.
Extends weak continuity of Yang-Mills connections to a broader class.
problem Weak compactness of -Yang-Mills connections.
method Compensation compactness argument applied to Yang-Mills fields.
result Weak continuity result extended to -Yang-Mills connections.
Paper explores two methods for optimal portfolio selection in financial markets.
problem Optimal portfolio selection for financial markets with jumps.
method Maximum principle and dynamic programming approach.
result Relationship between two methods and their adjoint processes.
This review article intends to introduce the reader to non-integrable geometric structures on Riemannian manifolds and invariant metric connections with torsion, and to discuss recent aspects of mathematical physics--in particular superstring theory--where these naturally appear. Connections with skew-symmetric torsion…
Recent theoretical results establish that time-consistent valuations (i.e. pricing operators) can be created by backward iteration of one-period valuations. In this paper we investigate the continuous-time limits of well-known actuarial premium principles when such backward iteration procedures are applied. We show tha…
Study nonholonomic systems with collisions using variational principles.
problem Variational problems on nonholonomic systems with collisions.
method Extended variational principle, introduced connection on principal bundles, applied Lagrange–Poincaré–Pontryagin reduction.
result Implicit Lagrange–d'Alembert–Pontryagin equations for nonholonomic systems with collisions.
Immersing quasi-Fuchsian surfaces of odd Euler characteristic in closed hyperbolic 3-manifoldsmath.GT
Paper shows odd Euler characteristic surfaces in hyperbolic 3-manifolds.
problem Embedding quasi-Fuchsian surfaces in closed hyperbolic 3-manifolds.
method Good pants method, enhanced connection principle.
result Every closed hyperbolic 3-manifold contains an immersed quasi-Fuchsian surface of odd Euler characteristic.
In this paper we introduce a generalisation of the notion of holonomy for connections over a bundle map on a principal fibre bundle. We prove that, as in the standard theory on principal connections, the holonomy groups are Lie subgroups of the structure group of the principle fibre bundle and we also derive a straight…
Paper finds a new principle for optimizing consumption and wealth using Tsallis entropy.
problem Optimal consumption-investment problem with recursive utility.
method Established connection to quadratic BSDE, derived stochastic maximum principle.
result Proved existence of optimal strategy and analyzed coupled system.
On the structure of compact Kähler manifolds with nonnegative holomorphic sectional curvaturemath.DG
The paper proves properties of complex manifolds with nonnegative holomorphic sectional curvature.
problem Characterizing compact Kähler manifolds with nonnegative holomorphic sectional curvature.
method Holonomy principle and geometric properties.
result Compact Kähler manifolds with nonnegative holomorphic sectional curvature are projective and rationally connected.
Symplectic connectionsmath.SG
This article is an overview of the results obtained in recent years on symplectic connections. We present what is known about preferred connections (critical points of a variational principle). The class of Ricci-type connections (for which the curvature is entirely determined by the Ricci tensor) is described in detai…
New variational principle found for non-variational differential equations.
problem Non-variational differential equations without variational multipliers.
method Connecting functional forms with antiexact differential forms to identify obstructions.
result Formulation of variational problem for non-variational equations.
Deep neural networks' infinite-width behavior approximated by Gaussian models.
problem Understanding the behavior of deep neural networks in the limit of infinite width.
method Using the Lindeberg exchange principle to approximate weights by Gaussian random variables.
result Quantitative bounds on the 2-Wasserstein distance between deep neural networks and Gaussian limits.
New principle for disentangling latent factors using sparse regularization.
problem Disentangling latent factors from complex data.
method Sparse regularization of latent mechanisms to induce disentanglement.
result Recovery of latent variables up to permutation under certain conditions.
The paper explores reflection principles for lightlike line segments on maximal surfaces.
problem Reflection property does not hold for lightlike line segments on maximal surfaces.
method Analyzes reflection properties for lightlike line segments connecting shrinking singularities.
result Shows a kind of reflection principle for lightlike line segments on maximal surfaces.
Classifies meromorphic affine connections on complex surfaces.
problem Investigating uniformization in higher dimensions with singularities.
method Extending work on holomorphic connections, classifying meromorphic connections on compact surfaces.
result Classification of meromorphic affine connections on compact complex surfaces.
By resorting to Noether's Second Theorem, we relate the generalized Bianchi identities for Lagrangian field theories on gauge-natural bundles with the kernel of the associated gauge-natural Jacobi morphism. A suitable definition of the curvature of gauge-natural variational principles can be consequently formulated in …
The paper establishes principles for initializing and designing GNNs with ReLU activations to avoid oversmoothing and correlation collapse.
problem Oversmoothing and correlation collapse in deep ReLU GNNs.
method The paper derives and validates three principles for initialization and architecture selection in finite width graph neural networks with ReLU activations.
result Correct initialization, residual aggregation operators, and residual connections significantly improve early training dynamics in deep ReLU GNNs.
New Einstein manifolds split into symmetric and compact parts.
problem Understanding Einstein manifolds with unimodular isometry groups.
method Theory of polar actions, Lie-theoretic arguments, and maximum principles.
result Negative Einstein manifolds split into symmetric and compact parts.
Upper bounds on nullhomotopy volumes in nilpotent spaces are refined.
problem Bounding volumes of nullhomotopies in nilpotent spaces.
method Extension of the Shadowing Principle to nilpotent spaces.
result Improved bounds on nullhomotopy volumes, nearly meeting simply connected settings.
We show that all vector bundles over CP^2 which are not spin admit a complete metric with nonnegative sectional curvature. In the proof we construct a nonnegatively curved metric on the corresponding principle bundle by showing that it admits a cohomogeneity one action with singular orbits of codimension 2. This is clo…
The study classifies prolongations up to Engel homotopy based on their formal data.
problem Classifying prolongations up to Engel homotopy.
method Reduction to formal data and study of homotopy type.
result The classification problem reduces to formal data when the turning number is large enough.
Reduction principles for proper actions on smooth manifolds.
problem Proper actions on smooth manifolds and their properties.
method Exhibit constructions and prove reduction principles for proper actions.
result Reduction principles hold for proper actions, polar actions, and copolarity.
It is shown that any irreducible analytic 1-flat -structure as well as any analytic torsion-free affine connection with irreducibly acting holonomy group can, in principle, be contstructed by twistor methods.
In this paper we show that the `quantization commutes with reduction' principle of Guillemin-Sternberg holds for the coadjoint orbits that parametrize the discrete series of a real connected semi-simple Lie group.
Study connects stationary spacetimes with pre-Randers metrics using Fermat's principle.
problem Understanding causal structures in stationary spacetimes.
method Relativistic Fermat's principle linking stationary spacetimes and pre-Randers metrics.
result Description of causal ladder in terms of pre-Randers metric elements.
Geometric derivation of Einstein equations from causal fermion systems.
problem Deriving Einstein's equations from a new theoretical framework.
method Analysis of causal fermion systems and causal action principle.
result Einstein equations derived from causal action principle.
New theorem connects probabilistic permanental point processes to Monge-Ampère equation.
problem Probabilistic interpretation of Monge-Ampère equation boundary value problem.
method Large deviation principles and optimal transport theory.
result Explicit rate function for permanental point processes large deviation.
This work uses statistical mechanics to explain AI learning.
problem Understanding the statistical principles behind AI learning.
method Starting from sample concentration behaviors, the study applies statistical mechanics principles to AI and machine learning.
result Exponential families and statistical quantities are key in AI and machine learning.
Alternative proof for non-existence of complete curves in differential strata.
problem Non-existence of complete algebraic curves in strata of holomorphic differentials.
method Using positivity of divisor classes on moduli spaces of curves.
result Alternative proof confirming Gendron's result on non-existence.
This paper is a review of the twistor theory of irreducible G-structures and affine connections. Long ago, Berger presented a very restricted list of possible irreducibly acting holonomies of torsion-free affine connections. His list was complete in the part of metric connections, while the situation with holonomies of…