Study bounds CMC surface index in 3-manifolds using energy.
problem Bounding the index of CMC surfaces in 3-manifolds.
method Energy comparison to prove linear upper bound.
result Linear upper bound on CMC surface index.
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48 results for “energy index”
Study bounds the index of minimal submanifolds using energy measures and Yang-Mills-Higgs equations.
problem Bounding the index of codimension 2 minimal submanifolds.
method Second inner variation of energy, convergence of energy measures, and stress-energy tensors.
result Bound the Morse index of the submanifold by the index of critical points.
Proves energy quantization for surfaces with bounded index.
problem Energy quantization for Willmore surfaces with bounded index.
method Translated the question to the conformal Gauss map's perspective and showed convergence in specific regions.
result Conformal Gauss map converges to a light-like geodesic in De Sitter space in neck or collar regions.
The paper proves a disk's energy minimizer is holomorphic and calculates its Morse index.
problem Analyzing the Morse index of a non-holomorphic disk in pseudoconvex domains.
method Proof of holomorphic minimizers and Morse index calculation.
result Non-holomorphic critical disks have a Morse index of at least n-1.
The paper bounds the energy index of harmonic Gauss maps on surfaces.
problem Bounding the energy index of harmonic Gauss maps on surfaces.
method Analyzes closed and complete non-compact surfaces in Lie groups with bi-invariant metrics.
result The energy index of the Gauss map is bounded by the topological genus.
We prove a conformally invariant estimate for the index of Schrödinger operators acting on vector bundles over four-manifolds, related to the classical Cwikel-Lieb-Rozenblum estimate. Applied to Yang-Mills connections we obtain a bound for the index in terms of its energy which is conformally invariant, and captures th…
The paper is devoted to finding conditions to the existence of a self-indexing energy function for Morse-Smale diffeomorphisms on a 3-manifold. These conditions involve how the stable and unstable manifolds of saddle points are embedded in the ambient manifold. We also show that the existence of a self-indexing energy …
Study introduces a new Allen-Cahn energy on hypersurfaces and analyzes its properties.
problem Analyzing geometric variations of the Allen-Cahn energy on hypersurfaces.
method Establishes Γ-convergence, computes variations, and analyzes the linearized equation.
result Shows that the index and nullity of the energy are related to the Allen-Cahn index and nullity.
Proves the index of a Möbius band in 4D ball equals 5.
problem Determining the Morse index of critical non-orientable surfaces.
method Comparison theorem between Steklov spectral index and energy index.
result Proves the index of critical Möbius band in equals 5.
In this article we study the second variation of the energy functional associated to the Allen-Cahn equation on closed manifolds. Extending well known analogies between the gradient theory of phase transitions and the theory of minimal hypersurfaces, we prove the upper semicontinuity of the eigenvalues of the stability…
Study finds bound on energy of minimal spheres on complex manifolds.
problem Finding bounds on energy of minimal spheres on complex manifolds.
method Proving existence of harmonic spheres with Morse index bound one.
result Sum of energies of minimal spheres realizes a geometric invariant width.
Study on harmonic maps from surfaces with energy bounds and neck domains.
problem Behavior of harmonic maps with bounded energy on complex domains.
method Analysis of a sequence of harmonic maps in generalized neck domains.
result Upper bound of energy density and study of nullity and index limits.
Stability of branched immersions with energy constraints.
problem Stability of branched Willmore immersions with bounded energy.
method Refined analysis of fourth-order differential operators with regular singularities.
result Sum of Morse index and nullity is lower semi-continuous.
The paper bounds the index of CMC surfaces with capillary boundary.
problem Bounding the index of CMC surfaces with capillary boundary.
method Comparison of second variations of area and energy, derived second variation formulae.
result The index is bounded linearly by genus, boundary components, and contact angle.
Comparison between Second Variation of Area and Second Variation of Energy of a Minimal Surfacemath.DG
The conformal parameterisation of a minimal surface is harmonic. Therefore, a minimal surface is a critical point of both the energy functional and the area functional. In this paper, we compare the Morse index of a minimal surface as a critical point of the area functional with its Morse index as a critical point of t…
Study index bounds for harmonic maps sequences with bubbles.
problem Upper and lower bounds of index and nullity for harmonic maps.
method Study limiting behavior of eigenfunctions of linearized operator; diagonalize index form with bilinear form varying with sequence.
result Obtain index bounds and show convergence of eigenfunctions on weak limit, bubbles, and neck regions.
New findings confirm parallels to De Giorgi's conjecture for phase transitions in higher dimensions.
problem Understanding phase transitions with bounded index in higher-dimensional spaces.
method Establishing parallels to De Giorgi's conjecture for general solutions of bounded Morse index.
result Finite index solutions to the Allen--Cahn equation in are one-dimensional, and this holds for all .
Minimal surfaces in spheres have unique energy properties.
problem Characterizing minimal surfaces in spheres based on their energy index and eigenvalues.
method Analyzing the second variations of area and energy for minimal immersions.
result New bounds on the energy index and eigenvalues for minimal surfaces in spheres.
THRML uses energy-based models for index tracking, reducing portfolio tracking error and improving returns.
problem NP-hard combinatorial optimization in portfolio optimization under cardinality constraints.
method THRML reformulates index tracking as probabilistic inference on an Ising Hamiltonian, using GPU-accelerated block Gibbs sampling.
result THRML achieves 4.31 percent annualized tracking error compared to 5.66-6.30 percent for baselines, with 128.63 percent total return.
The identity map of certain Einstein manifolds is stable in both energy and bienergy.
problem Stability of the identity map in Einstein manifolds.
method Investigation of conformal-biharmonic stability compared to harmonic stability.
result The conformal-biharmonic index coincides with the harmonic index, except for the 4D Euclidean sphere.
Inspired by work of Ejiri-Micallef on closed minimal surfaces, we compare the energy index and the area index of a free-boundary minimal surface of a Riemannian manifold with boundary, and show that the area index is controlled from above by the area and the topology of the surface. Combining these results with work of…
Study of Dirac-Witten operator on Lorentzian manifolds under dominant energy condition.
problem Detecting non-trivial homotopy groups in spaces of initial data under strict dominant energy condition.
method Use index theory and Lorentzian Hitchin's α-invariant to analyze Dirac-Witten operator.
result Kernel of Dirac-Witten operator is non-trivial only if fundamental group is virtually solvable of derived length at most 2.
In recent years there has been an advent of quanto options in energy markets. The structure of the payoff is rather a different type from other markets since it is written as a product of an underlying energy index and a measure of temperature. In the HJM framework, by adopting the futures energy dynamics, we use the M…
Federated learning calibrates insurance indices from renewable energy producers' data.
problem Calibrating parametric insurance indices under heterogeneous renewable energy production losses.
method Federated learning framework using Tweedie GLMs and distributed optimization.
result Federated learning recovers comparable index coefficients under moderate heterogeneity.
Study finds surfaces in spherical caps that maximize modified energy.
problem Geometry of surfaces with free boundaries and capillary conditions.
method Monotonicity formulae and energy maximization analysis.
result Capillary minimal surfaces maximize a modified energy in their conformal orbit.
Study of minimal surfaces and their inversion properties in R^n.
problem Properties of complete minimal surfaces with finite total curvature.
method Inversion and conformal compactification to study stationary Willmore energy.
result Exact Willmore index for inverted minimal spheres and real projective planes.
Stable solutions to a specific equation are one-dimensional.
problem Stability and dimensionality of solutions to the Allen-Cahn equation.
method Analysis of stable solutions with bounded energy density.
result Stable solutions to the Allen-Cahn equation are one-dimensional.
In some recent papers, the relations existing between the metric properties of Randers spaces and the conformal geometry of stationary Lorentzian manifolds were discovered and investigated. In this note, we focus on the equality between the index of a geodesic in a Randers space and that of its lightlike lift in the as…
Perturbed geodesics are trajectories of particles moving on a semi-Riemannian manifold in the presence of a potential. Our purpose here is to extend to perturbed geodesics on semi-Riemannian manifolds the well known Morse Index Theorem. When the metric is indefinite, the Morse index of the energy functional becomes inf…
Strict plurisubharmonicity of the energy on Teichmüller space associated to Hitchin representationsmath.DG
Strict plurisubharmonicity proven for Teichmüller energy on Hitchin representations.
problem Proving strict plurisubharmonicity of Teichmüller energy for Hitchin representations.
method Analyzing energy functional on Teichmüller space associated to Hitchin representations.
result Strict plurisubharmonicity of energy functional proven.
The study examines the index of MOTS in Kerr-Newman-de Sitter spacetime and its relation to mass and charge.
problem Investigating the index of MOTS in Kerr-Newman-de Sitter spacetime.
method Analyzing the spatial cross section of the cosmological horizon in the Kerr-Newman-de Sitter spacetime, proving index bounds and establishing area-charge estimates.
result Established bounds on the index of MOTS and a connection between MOTS with index one and General Relativity.
In this paper, we model the impact of oil price volatility on Tehranstock and industry indices in two periods of international sanctions and post-sanction. To analyse the purpose of study, we use Feed-forward neural net-works. The period of study is from 2008 to 2018 that is split in two periods during international en…
Improved diffusion models using energy distillation and sequential Monte Carlo.
problem Training instability and inferior performance in energy parameterized diffusion models.
method Introduced a novel training regime for energy functions through distillation of pre-trained diffusion models, and cast the sampling procedure as a Feynman Kac model.
result Demonstrated improved performance and new sampling techniques.
Stability of Morse index for Yang-Mills connections in 4D.
problem Stability of critical points in Yang-Mills energy relaxation.
method Establishing lower semi-continuity of Morse index and upper continuity of Morse index plus nullity.
result Yang-Mills fields are more stable than harmonic maps in 4D.
J.Eells and L. Lemaire introduced -harmonic maps, and Wang Shaobo showed the first variation formula. In this paper, we give the second variation formula of -energy, and give a notion of index, nullity and weakly stable. We also study -harmonic maps into the product Riemannian manifold, and -harmonic curves…
We consider unbranched Willmore surfaces in the Euclidean space that arise as inverted complete minimal surfaces with embedded planar ends. Several statements are proven about upper and lower bounds on the Morse Index - the number of linearly independent variational directions that locally decrease the Willmore energy.…
Improved Morse Index Stability for Sequences of Harmonic Maps from Degenerating Riemann Surfacesmath.DG
Stability of Morse index for harmonic maps on degenerating surfaces analyzed.
problem Analyzing stability of Morse index for harmonic maps on degenerating Riemann surfaces.
method Analysis of second variation of energy, identification of conditions for upper semicontinuity, explicit contribution of geodesics.
result Sharper control of spectrum of Jacobi operator, explicit contribution of geodesic segments to Morse index.
This study examines local co-movements in energy, agriculture, and metal markets using copulas.
problem Identifying local dependencies and asymmetries in energy, agriculture, and metal markets.
method Non-parametric mixture copula and copula-based local Kendall's tau approach.
result Increased co-movements in extreme situations, asymmetric local dependence, and diversification potential.
The study characterizes and studies stability of biharmonic hypersurfaces in complex space forms.
problem Characterizing and studying biharmonic hypersurfaces in complex space forms.
method Characterizing hypersurfaces as critical points of a higher order energy functional.
result Existence and non-existence results for and .
Develops a PDE approach to constructing nontrivial anisotropic surfaces.
problem Min-max construction of anisotropic surfaces.
method PDE-based approach to anisotropic surface energies.
result Construction of an anisotropic min-max hypersurface.
The dominant energy condition imposes a restriction on initial value pairs found on a spacelike hypersurface of a Lorentzian manifold. In this article, we study the space of initial values that satisfy this condition strictly. To this aim, we introduce an index difference for initial value pairs and compare it to its c…
In this work, a version of Fermat's principle for causal curves with the same energy in time orientable Finsler spacetimes is proved. We calculate the secondvariation of the {\it time arrival functional} along a geodesic in terms of the index form associated with the Finsler spacetime Lagrangian. Then the character of …
Paper proves existence of minimal doublings on surfaces with specific properties.
problem Existence of minimal doublings on surfaces with given properties.
method Variational approach to finding nondegenerate critical points of a Coulomb-type energy.
result Proves existence of minimal doublings for surfaces of index one in a generic 3-manifold.
We present a connection between minimal surfaces of index one and General Relativity. First, we show that for a certain class of (electro)static systems, each of its unstable horizons is the solution of a one-parameter min-max problem for the area functional, in particular it has index one. We also obtain an inequality…
Memory Organization for Energy-Efficient Learning and Inference in Digital Neuromorphic Acceleratorscs.NE
Improves energy efficiency of neuromorphic hardware by optimizing memory organization and encoding schemes.
problem Energy inefficiency in neuromorphic hardware, especially in digital accelerators.
method Synthesized controller and memory for different encoding schemes, introduced functional encoding for structured connectivity.
result Functional encoding offers a 58% reduction in energy for weight updates in convolutional layers.
Following the thermodynamic formulation of multifractal measure that was shown to be capable of detecting large fluctuations at an early stage, here we propose a new index which permits us to distinguish events like financial crisis in real time . We calculate the partition function from where we obtain thermodynamic q…
Wavelet analysis reveals financialization effects on oil-food price correlation.
problem Investigating the correlation between oil and food prices and their determinants.
method Wavelet analysis and energy-based measures to differentiate high and low frequency movements.
result Significant local correlation between food and oil is due to financialization and emerging economies' demand.
The study finds that firm membership in flagship indices and TCFD endorsement are strong predictors of a wider Disclosure-Performance Gap.
problem The Aggregate Confusion hypothesis and the measurement of greenwashing in environmental disclosures.
method The study uses a Disclosure-Performance Gap (DPG) model to measure the divergence between voluntary environmental disclosures and realised emissions performance for 200 large European firms. The model selection process involved multiple stages and robust standard errors.
result Firm membership in flagship indices and TCFD endorsement are strong predictors of a wider gap, while renewable energy use and environmental capital expenditure significantly narrow the gap.