Proves interior C2 estimate for a specific equation in 3D.
problem Proving interior C2 estimate for a specific equation in 3D.
method Proves a priori interior C2 estimate for σ_2 = f in R3.
result Generalizes Warren-Yuan's result with a C2 estimate.
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32 results for “C2”
We prove that a riemannian metric on the 2-sphere or the projective plane can be C2-approximated by a smooth metric whose geodesic flow has an elliptic closed geodesic.
The Clifford group for 2 qubits is divided into 20 orbits, each with 4608 matrices.
problem Understanding the structure of the Clifford group for 2 qubits.
method Equivalence relation based on local Clifford gates and analysis of orbits.
result The Clifford group for 2 qubits is divided into 20 orbits, each with 4608 matrices.
New algorithm for C2-splines on curved spaces.
problem Need for spline interpolation on curved, non-Euclidean space.
method Iterative algorithm for C2-splines on Riemannian symmetric spaces.
result New method surpasses Riemannian cubics in numerical tractability and computational efficiency.
New algorithm boosts classification for imbalanced data.
problem Accurately classifying observations in severely imbalanced datasets.
method SAMME.C2 algorithm blending boosting and cost-sensitive techniques.
result Consistently superior performance in imbalanced classification problems.
Criteria for extending degree-2 Azumaya algebras with C2-actions over curves.
problem Determining when degree-2 Azumaya algebras with C2-actions extend to entire curves.
method Criteria for extension of algebra and new condition for extension with action, testable by computer algebra systems.
result New conditions for extending degree-2 Azumaya algebras with C2-actions over curves.
Establishes interior C2 estimates for convex solutions to curvature equations.
problem Interior regularity of convex solutions to curvature equations.
method Interior estimates for scalar curvature and -Hessian equations.
result Interior curvature estimates for convex solutions and isometric hypersurfaces.
Study optimal inequality for contact CR-warped product submanifolds in cosymplectic space forms.
problem Optimal inequality for contact CR-warped product submanifolds in cosymplectic space forms.
method Using Gauss and Codazzi equations, prove an optimal inequality.
result Prove an optimal inequality for contact CR-warped product submanifolds.
Differentiable sorting and rank normalization are incompatible, with specific conditions for admissibility.
problem Incompatibility between differentiable sorting and rank normalization.
method Formalized admissibility through monotone invariance, batch independence, and rank-space stability conditions.
result Different gap-sensitive and batchwise relaxations of rank normalization violate the conditions for admissibility.
The paper derives Gauss-Bonnet theorems for deformed connections in affine and rigid motions groups.
problem Computing curvature and geodesic curvature for surfaces and curves in affine and rigid motions groups.
method Defined deformed Schouten-Van Kampen connections, computed Gaussian curvature limits, and signed geodesic curvature.
result Derived Gauss-Bonnet theorems for deformed connections in affine and rigid motions groups.
We define disentanglement in generative models and prove it's related to identifiable factors.
problem Understanding disentanglement in generative models like VAEs and GANs.
method Characterized disentanglement in smooth generative pushforward models using the SVD of the Jacobian.
result Disentanglement is identifiable under certain conditions on the generator, promoting separable factors.
Stable saddle solutions found for specific dimensions of the Allen-Cahn equation.
problem Stability of saddle solutions for the Allen-Cahn equation in specific dimensions.
method Analyzing the Simons cone and energy functional to confirm saddle solutions' stability.
result Stable saddle solutions found for .
We provide a measure based topology for certain unions of C2 rectifiable submanifolds of mixed dimensions in Rn. In this topology lower dimensional sets remain in the limit as measures when higher dimensional sets collapse down to them. For example a decreasing sequence of spheres may have a limit consisting of just a …
Proofs a theorem using basic geometric tools.
problem C2-rectifiability problem
method Elementary geometric measure theory and topology
result Gives a proof of Alberti's Luzin-type theorem
Study on transnormal functions and their level sets on Finsler manifolds.
problem Understanding transnormal functions and their geometric properties on Finsler manifolds.
method Proving smoothness of focal varieties and regular level sets of transnormal functions.
result Focal varieties of a C2 transnormal function are smooth submanifolds and regular level sets are tubes over these varieties.
Revises Schwarzschild manifold rigidity proof for spin manifolds.
problem Rigidity of Schwarzschild manifold for spin manifolds.
method Spinorial proof approach.
result Generalizes and includes classical and recent black hole uniqueness theorems.
Foliated Milnor conjecturemath.GT
Proves fundamental group of certain manifolds is finitely generated and almost abelian.
problem Fundamental group of specific manifolds.
method Nonnegative Ricci curvature foliation approach.
result Confirms Milnor conjecture for certain manifolds.
Smooth knots in complex hyperbolic plane limit sets to chains or R-circles.
problem Characterizing limit sets of knots in complex hyperbolic geometry.
method Analyzing embeddings of knots as limit sets of discrete subgroups of PU(2, 1).
result Knots are either chains or R-circles as limit sets.
Let be a smooth closed hypersurface with non-negative Ricci curvature, isometrically immersed in a space form. It has been proved in \cite{P}, \cite{CZ}, and \cite{C2} that there are some inequalities on which measure the stability of closed umbilical hypersurfaces or more generally, closed hypersurfaces …
Solves the Dirichlet problem for minimal hypersurfaces on Riemannian manifolds.
problem Finding conditions for solvability of the Dirichlet problem with Lipschitz boundary data.
method Extends Williams' result to Riemannian manifolds, focusing on smallness conditions.
result Establishes existence of solutions under certain boundary data conditions.
Improved risk assessment for UBI using telematics data and AdaBoost.
problem Class imbalance in predicting claims frequency for UBI.
method Cost-sensitive multi-class AdaBoost (SAMME.C2) algorithm.
result SAMME.C2 outperforms other models in handling class imbalances.
Any strictly pseudoconvex domain in C2 carries a complete Kahler-Einstein metric, the Cheng-Yau metric, with ``conformal infinity'' the CR structure of the boundary. It is well known that not all CR structures on the 3-sphere arise in this way. In this paper, we study CR structures on the 3-sphere satisfying a differen…
Effective Cartan-Tanaka connections on C6-smooth strongly pseudoconvex hypersurfaces M3 of C2math.DG
In a recent expository article (Notices of the AMS, 58 (2011), no. 1, 20-27), Ezhov, McLaughlin and Schmalz showed how to perform in an effective way Tanaka's prolongation procedure valid generally for filtered structures of constant type when the distribution is equipped with an integrable complex structure, so as to …
Let G be a finitely generated group having the property that any action of any finite-index subgroup of G by homeomorphisms of the circle must have a finite orbit. (By a theorem of E.Ghys, lattices in simple Lie groups of real rank at least two have this property.) Suppose that such a G acts on a compact manifold M by …
The paper examines sequences of solutions to Seiberg-Witten systems in 4D manifolds.
problem Analyzing sequences of solutions to Seiberg-Witten systems in 4D manifolds.
method Investigates the behavior of sequences of solutions to Seiberg-Witten-like equations for Hermitian connections and spinor sections.
result Provides insights into the behavior of sequences of solutions to Seiberg-Witten systems in 4D manifolds.
Proves existence and uniqueness of solutions to a quaternionic Monge-Ampère equation.
problem Solving the quaternionic Monge-Ampère equation for -quaternionic plurisubharmonic functions on a hyperKähler manifold.
method Proves existence and uniqueness of solutions using a Cherrier-type inequality and and estimates.
result Obtains smooth solutions to the quaternionic Monge-Ampère equation.
We calculate the first and the second variation formula for the sub-Riemannian area in three dimensional pseudo-hermitian manifolds. We consider general variations that can move the singular set of a C^2 surface and non-singular variation for C_H^2 surfaces. These formulas enable us to construct a stability operator fo…
Let M be a differentiable manifold. We say that a tensor field g defined on M is non-regular if g is in some local Lp space or if g is continuous. In this work we define a mollifier smoothing g_t of g that has the following feature: If g is a Riemannian metric of class C2, then the Levi-Civita connection and the Rieman…
Active Kriging Monte Carlo simulation method with conformal certification for failure probability estimation
problem Failure probability estimation in structural reliability analysis
method Active learning framework with conformal prediction
result Improved uncertainty quantification and reliability of failure probability estimates
ParamBoost uses gradient boosting to create interpretable non-linear models with constraints.
problem Creating interpretable non-linear models with expert knowledge constraints.
method Gradient Boosting of cubic polynomials with specified constraints.
result ParamBoost outperforms state-of-the-art GAMs in real-world datasets.
Cohomology Vanishing for Free Boundary -Minimal Submanifolds in Gaussian-Weighted Euclidean Ballsmath.DG
The paper proves cohomology vanishing for a specific type of minimal submanifolds in a weighted Euclidean ball.
problem Proving cohomology vanishing for free boundary -minimal submanifolds in Gaussian-weighted Euclidean balls.
method The proof uses a weighted Hardy inequality, cancellation in the weighted Weitzenböck curvature operator, and a boundary reduction.
result The space of tangential -harmonic -forms vanishes, leading to .
The most recent update of financial option models is American options under stochastic volatility models with jumps in returns (SVJ) and stochastic volatility models with jumps in returns and volatility (SVCJ). To evaluate these options, mesh-based methods are applied in a number of papers but it is well-known that the…