We investigate probability measures with finite pluricomplex energy. We give criteria insuring that a given measure has finite energy and test these on various examples. We show that this notion is a biholomorphic but not a bimeromorphic invariant.
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48 results for “pluricomplex energy”
New probabilistic constructions for Kähler-Einstein metrics.
problem Finding Kähler-Einstein metrics on complex algebraic varieties.
method Microcanonical measures and maximum entropy principles.
result Novel characterizations and evolution equations.
We show that degenerate complex Monge-Ampere equations in a big cohomology class of a compact Kaehler manifold can be solved using a variational method independent of Yau's theorem. Our formulation yields in particular a natural pluricomplex analogue of the classical logarithmic energy of a measure. We also investigate…
Hypercomplex limits of pluricomplex structures and the Euclidean limit of hyperbolic monopolesmath.DG
We discuss the Euclidean limit of hyperbolic SU(2)-monopoles, framed at infinity, from the point of view of pluricomplex geometry. More generally, we discuss the geometry of hypercomplex manifolds arising as limits of pluricomplex manifolds.
We continue our study of the Complex Monge-Ampère Operator on the Weighted Pluricomplex energy classes. We give more characterizations of the range of the classes by the Complex Monge-Ampère Operator. In particular, we prove that a non-negative Borel measure is the Monge-Ampère of a unique function …
Motivated by strong desire to understand the natural geometry of moduli spaces of hyperbolic monopoles, we introduce and study a new type of geometry: pluricomplex geometry. It is a generalisation of hypercomplex geometry: we still have a 2-sphere of complex structures, but they no longer behave like unit imaginary qua…
This is the first paper in a series of investigation of the pluripotential theory on Teichmüller space. The main purpose of this paper is to give an alternative approach to the Krushkal formula of the pluricomplex Green function on Teichmüller space. We also show that Teichmüller space carries a natural stratified stru…
Paper introduces a new Poisson kernel for strongly pseudoconvex domains.
problem Developing a new mathematical tool for strongly pseudoconvex domains.
method Introducing a maximal plurisubharmonic function called the pluricomplex Poisson kernel.
result The pluricomplex Poisson kernel shares properties with the classical Poisson kernel and reproduces pluriharmonic functions.
It is shown that, on a compact Kahler manifold with boundary, the singularities of the pluricomplex Green's function with multiple poles can be prescribed to be of the form at each pole, where are arbitrary local holomorphic functions with the pole as their only common zero. The pr…
In this paper, we prove a estimate for solutions of complex Monge-Ampère equations on compact almost Hermitian manifolds. Using this estimate, we show existence of solutions to the degenerate Monge-Ampère equations, the corresponding Dirichlet problems and the singular Monge-Ampère equatio…
New geometric conditions ensure compactness of -Neumann problem.
problem Compactness of -Neumann operator on specific domains.
method Introduced new geometric conditions for a class of domains, proving compactness equivalence to boundary properties.
result Compactness of -Neumann operator equivalent to boundary lack of analytic varieties.
We prove that if a smoothly bounded strongly pseudoconvex domain , , admits at least one Monge-Ampère exhaustion smooth up to the boundary (i.e. a plurisubharmonic exhaustion , which is at all points except possibly at the unique minimum poi…
Holographic energy equals Hamiltonian energy.
problem Equating holographic and Hamiltonian energies.
method Relative holographic and Hamiltonian energy comparison.
result Holographic energy is identical to Hamiltonian energy.
Optimizes energy efficiency in wireless sensor networks with limited information.
problem Maximizing energy efficiency in energy harvesting wireless sensor networks with limited channel state information.
method Modeling as a Multi-Armed Bandits problem and developing an Upper Confidence Bound algorithm.
result Significant gains in energy efficiency compared to benchmark schemes.
Reduces energy for 4D submanifolds in R^n.
problem Energy reduction for 4D submanifolds in R^n.
method Connected sum energy reduction for fourth-order Willmore energy.
result Established a connected sum energy reduction for the fourth-order Willmore energy.
Let be the energy of some knot for any from certain class of functions. The problem is to find knots with extremal values of energy. We discuss the notion of the locally perturbed knot. The knot circle minimizes some energies and maximizes some others. So, is there any energy such that the circle ne…
New formula connects Loewner energy to moving frames' renormalised energy.
problem Calculating Loewner energy of Jordan curves.
method Using renormalised energy of moving frames.
result Loewner energy as Kähler potential for Weil-Petersson space.
The paper proves -convergence of discrete tangent-point energies to continuous energies and ropelength, with applications to biarc curves.
problem Proving convergence of discrete tangent-point energies to continuous energies and ropelength.
method Using biarc curves and interpolation, the paper proves -convergence of discretized tangent-point energies to the continuous tangent-point energies and ropelength functional.
result Discrete almost minimizing biarc curves converge to ropelength minimizers and minimizers of continuous tangent-point energies.
Quantizes Willmore energy in Riemannian manifolds with bounded energy and area.
problem Quantization of Willmore energy in bounded energy and area conditions.
method Uniform boundedness of Willmore energy and area, weak convergence of maps, and conformal structures in compact domain.
result Quantization of Willmore energy holds under specified conditions.
Paper finds relations between Willmore-type energies, weighted areas, and vertical potential energies for cylindrical critical points.
problem Tackles relations between three types of energy functions for cylindrical critical points.
method Uses differential equations and critical point analysis for Willmore-type energies and weighted areas.
result Generating curves coincide for Willmore-type energies and weighted areas, and similar results hold for Willmore-type energies and vertical potential energies.
Energy-efficient DL inference for IoT devices reduces power consumption and improves performance.
problem Energy inefficiency in deep learning models for IoT devices.
method Energy-aware early exiting policy to balance energy consumption and inference accuracy.
result Accuracy and service rate improved up to 25% and 35% respectively.
Abstract reviews hyperbolic positive energy theorems.
problem Analyzing positive energy theorems for hyperbolic spaces.
method Review of existing literature on asymptotically hyperbolic manifolds.
result Summarizes positive energy theorems for hyperbolic spaces.
Discrete geometry model approximates Willmore energy.
problem Approximating the Willmore energy for triangulated surfaces.
method A discrete energy defined in the spirit of discrete differential geometry converges to the Willmore energy.
result The discrete energy converges to the Willmore energy in the sense of -convergence.
Enhanced tabular benchmarks for energy-efficient neural architecture search.
problem Energy consumption in deep learning models.
method Introducing EC-NAS, an enhanced tabular benchmark with energy consumption data.
result EC-NAS reveals a balance between energy usage and accuracy in neural architecture search.
Quantum computing offers energy savings over classical computing.
problem Energy efficiency in computing services.
method Cournot competition model constrained by energy usage.
result Quantum computing firms can outperform classical counterparts in energy efficiency.
Investigates a new four-dimensional energy related to Willmore energy.
problem Exploring a new conformally invariant energy in four dimensions.
method Computed first variation, applied Noether's theorem, investigated other generalizations.
result Critical points of the new energy are smooth and do not include minimal hypersurfaces.
Derives energy-momentum tensor from Standard Model, examines energy conditions.
problem Validating energy conditions in the context of the Standard Model.
method Geometric variational problem on globally hyperbolic manifold, deriving energy-momentum tensor.
result Validates various energy conditions in general relativity.
Study of critical tori for mean curvature energies in Killing submersions.
problem Analyzing surface energies in Killing submersions.
method Symmetry reduction and binormal evolution of critical curves.
result Construction of vertical tori critical for mean curvature energies.
Study on infinite energy maps from surfaces to CAT(0) spaces.
problem Harmonic maps with infinite energy from Riemann surfaces to CAT(0) spaces.
method Estimates of energy growth near punctures, proof of uniqueness.
result Precise estimates of energy growth near punctures and proof of uniqueness of harmonic maps.
Advances in renewable energy generation and introduction of the government targets to improve energy efficiency gave rise to a concept of a Zero Energy Building (ZEB). A ZEB is a building whose net energy usage over a year is zero, i.e., its energy use is not larger than its overall renewables generation. A collection …
Proposes linking energy and force uncertainty in deep learning potentials.
problem Uncertainty in predicted energies and forces in machine learning models.
method Introduces a spatially correlated noise process to link energy and force uncertainty.
result Demonstrates the approach on molecular datasets, linking energy and force uncertainties.
Versatile model for High Energy Physics events.
problem Modeling complex interactions in high-energy physics data.
method Energy-based probabilistic model with multi-purpose architecture.
result Achieves success in diverse applications like simulation, anomaly detection, and particle identification.
Traditional centralized energy systems have the disadvantages of difficult management and insufficient incentives. Blockchain is an emerging technology, which can be utilized in energy systems to enhance their management and control. Integrating token economy and blockchain technology, token economic systems in energy …
Paper proposes new loss functions for training energy networks.
problem Challenges in computing gradients for training energy networks.
method Proposes generalized Fenchel-Young losses for efficient gradient computation.
result Demonstrates the calibration of excess risk for linear-concave energies.
New invariant for 4D hypersurfaces ensures smooth critical points.
problem Understanding smoothness of curvature energies on 4D hypersurfaces.
method Developed a new conformally invariant energy.
result Critical points of new energy are smooth.
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.
Researchers establish bounds and continuity of decomposed Möbius energies using cosine formula.
problem Estimating the bounds and continuity of decomposed Möbius energies.
method Using the cosine formula to evaluate upper and lower bounds and modulus of continuity of decomposed energies.
result Affirmative answer to the question of estimating decomposed energies using the cosine formula.
Stability of a new map derived from the equator map is analyzed.
problem Stability of a new map derived from the equator map.
method Detailed stability analysis of the generalized equator map as a critical point of the extrinsic k-energy and p-energy.
result Established generalizations of classical (in)stability results.
The Möbius energy, defined by O'Hara, is one of the knot energies, and named after the Möbius invariant property which was shown by Freedman-He-Wang. The energy can be decomposed into three parts, each of which is Möbius invariant, proved by Ishizeki-Nagasawa. Several discrete versions of Möbius energy, that is, corres…
Triangulates surfaces with bounded energy using diffeomorphisms.
problem Triangulating surfaces with bounded Kolasinski--Menger energy.
method Uses bounded distortion diffeomorphisms of subsets of a plane.
result Triangulation with bounded number of triangles.
In this short article, we extend the cosine formula for the Möbius energy to generalized O'Hara energies. The newly derived formula gives us a condition for which the right circle minimizes the energy under the length-constraint. Furthermore, it shows us how far the energy is from the Möbius invariant property.
Study on bending knots and energy changes in 3D space.
problem Understanding energy changes in knots under small deformations.
method Analyzes infinitesimal bending of knots and energy changes using Willmore and Mobius energies.
result Changes in energy under small deformations of knots have been quantified.
Extends denoising and score estimation to energy models via Tweedie's formula.
problem Linking denoising and score estimation for a wider range of distributions.
method Derives a fundamental identity connecting energy score derivatives and scores.
result Establishes a new identity for energy scores analogous to Tweedie's formula.
We define a new class of knot energies (known as renormalization energies) and prove that a broad class of these energies are uniquely minimized by the round circle. Most of O'Hara's knot energies belong to this class. This proves two conjectures of O'Hara and of Freedman, He, and Wang. We also find energies not minimi…
In this paper, we analyzed the physical meaning of scalar curvatures for a generalized Riemannian space. It is developed the Madsen's formulae for pressures and energy-densities with respect to the corresponding energy-momentum tensors. After that, the energy-momentum tensors, pressures, energy-densities and state-para…
CityTFT models urban building energy using a data-driven approach.
problem Current UBEM methods are time-consuming and based on physics.
method CityTFT uses a TFT framework with an augmented loss function.
result CityTFT predicts energy demands with high accuracy.
Study generalizes Möbius energy to non-smooth sets in arbitrary dimensions.
problem Investigate Möbius-invariant energies on non-smooth subsets of arbitrary dimensions.
method Show local finite energy implies embedded Lipschitz submanifold, and low fractional Sobolev regularity guarantees finite energy.
result Local graph structure of low fractional Sobolev regularity on a set is sufficient to guarantee finite energy.
Defines a new energy for submanifolds, comparing to Willmore energy.
problem Finding new conformally invariant energies for submanifolds.
method Coupling tractor connection to GJMS operators for higher-dimensional analogues.
result Shows comparison with existing energy in 4D.