Global homeomorphism constructed from 3D Ricci limit spaces.
problem Global regularity of 3D Ricci limit spaces.
method Local pyramid Ricci flows and partial Ricci flows.
result Global homeomorphism to a smooth manifold.
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169,181 papers · 148 categories
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48 results for “pyramid Ricci flows”
The paper develops a new Ricci flow method in higher dimensions.
problem Constructing a Ricci flow on non-collapsed -limit spaces.
method Constructing a pyramid Ricci flow on a subset of space-time.
result Non-collapsed -limit spaces are globally homeomorphic to smooth manifolds.
New discrete conformal structures on surfaces with boundary, proving global rigidity and constructing hyperbolic metrics.
problem Creating new discrete conformal structures on surfaces with boundary.
method Introducing new discrete conformal structures, proving global rigidity using variational principles, and introducing combinatorial curvature flows.
result Global rigidity of new discrete conformal structures and effective algorithms for constructing hyperbolic metrics.
SPF uses a hierarchical approach to efficiently emulate climate changes.
problem Slow and unstable climate emulation for long horizons.
method Spatiotemporal Pyramid Flows (SPF) model data hierarchically across spatial and temporal scales.
result SPF outperforms flow matching baselines and pre-trained models on ClimateBench.
The paper analyzes Laplacian pyramids for extending and denoising discrete functions.
problem Analyzing conditions for convergence and stability of Laplacian pyramids.
method Investigates Laplacian pyramids for extension and denoising, providing convergence conditions and stability bounds.
result Mild conditions are provided under which the Laplacian pyramids algorithm converges and stability bounds are proven.
Improves instance segmentation accuracy by integrating low-level features.
problem Low-level features enhance instance localization accuracy.
method Integrates low-level features into all layers of a feature pyramid network.
result Consistent improvement in precision on COCO Dataset.
A novel approach for augmenting histopathological images by blending Gaussian-Laplacian pyramids.
problem Data imbalance and inter-patient variability in histopathological images.
method Image blending using Gaussian-Laplacian pyramids to distribute inter-patient variability.
result Promising gains in performance compared to existing data augmentation techniques.
Pyramid Attention Networks improve image restoration by leveraging self-similarities across scales.
problem Lack of full exploitation of self-similarities in image restoration by recent deep learning methods.
method Introduces a Pyramid Attention module that processes multi-scale feature correspondences to borrow clean signals from coarser levels.
result Pyramid Attention module achieves state-of-the-art results in various image restoration tasks.
Simulation reveals relationships in stock market pyramid schemes.
problem Understanding pyramid scheme behavior in stock markets.
method Agent-based simulation with four investor types and parameters.
result Relationships between main fund's rate of return and trend investors' proportion.
ADAVI tackles variational inference for large HBM models in neuroimaging.
problem Large, pyramidally-organized HBM models in neuroimaging studies.
method Automatic dual amortized variational inference using neural networks and attention-based hierarchical encoding.
result Significantly reduced parameterization of the variational family, maintaining expressivity.
A new pyramidal diffusion model speeds up image generation.
problem Training and evaluating diffusion models are time-consuming.
method Introduces a pyramidal diffusion model with a single score function.
result Generates high-resolution images from low-resolution starting points efficiently.
Single wide layer followed by a pyramidal structure ensures global convergence in deep networks.
problem Ensuring global convergence in deep neural networks with limited width constraints.
method Proves that a single wide layer followed by a pyramidal structure guarantees global convergence for over-parameterized networks.
result Single wide layer of width suffices for global convergence in deep networks with constant-width remaining layers.
We generalize the observable diameter and the separation distance for metric measure spaces to those for pyramids, and prove some limit formulas for these invariants for a convergent sequence of pyramids. We obtain various applications of our limit formulas as follows. We have a criterion of the phase transition proper…
By formulating N = 1, 2, 4, 8, D = 3, Yang-Mills with a single Lagrangian and single set of transformation rules, but with fields valued respectively in R,C,H,O, it was recently shown that tensoring left and right multiplets yields a Freudenthal-Rosenfeld-Tits magic square of D = 3 supergravities. This was subsequently…
TP-AIS improves sampling efficiency over existing methods.
problem Efficient sampling from complex probability distributions.
method Iterative sampling using a tree pyramid structure.
result TP-AIS outperforms DM-PMC, M-PMC, and LAIS.
Study ancient Ricci flows with nonnegative Ricci curvature and their asymptotic geometry.
problem Understanding the asymptotic geometry of ancient Ricci flows with nonnegative Ricci curvature.
method Analyze tangent flows at infinity and use estimates for noncollapsed F-limit metric solitons.
result Two dichotomy theorems for ancient Ricci flows: either the asymptotic volume ratio is zero or every tangent flow is a Ricci flat cone.
Study stability and instability of Ricci-flat metrics under generalized Ricci flow.
problem Stability and instability of Ricci-flat metrics under Ricci flow.
method Analysis of generalized Ricci flow for Ricci-flat metrics and vanishing 3-forms.
result Dynamical stability and instability results for Ricci-flat metrics and vanishing 3-forms.
Smooth 3D flows from non-smooth starting points.
problem Creating smooth Ricci flows from non-smooth initial conditions.
method Generalized singular Ricci flow applied to 3D complete manifolds.
result Existence of smooth Ricci flows starting from non-smooth initial conditions.
Some Results on Ricci Flowmath.DG
Paper introduces Ricci flow and its properties.
problem Exploring geometric curvature tensors under Ricci flow.
method Introducing Ricci flow and analyzing its properties.
result Found deformation of geometric curvature tensors under Ricci flow.
Study smoothings of ellipsoid intersections with singularities.
problem Smooth singular intersections of ellipsoids.
method Study 3D manifolds with singularities as small covers of Coxeter polyhedral orbifolds.
result Introduce -pyramitoid to generalize -pyramids.
Parabolic frequency monotonicity on Ricci flow and Ricci-harmonic flow with bounded curvaturesmath.DG
The paper examines how parabolic frequency behaves under Ricci flow and Ricci-harmonic flow on manifolds.
problem Understanding the behavior of parabolic frequency under Ricci flow and Ricci-harmonic flow.
method Investigates the monotonicity of parabolic frequency for solutions of linear and heat equations with bounded curvatures.
result Establishes monotonicity results for parabolic frequency under specific curvature conditions.
Improves speaker verification for variable-duration utterances using a feature pyramid module.
problem Improving robustness for variable-duration utterances in speaker verification.
method Integrates a feature pyramid module into multi-scale aggregation to enhance speaker-discriminative information from multiple layers.
result Improves performance for both short and long utterances compared to state-of-the-art approaches.
Paper compares Ricci flow volume changes and applies to Kähler-Ricci flow.
problem Volume comparison in Ricci flow and convergence of Kähler-Ricci flow.
method Derives a new relative volume comparison estimate and applies it to Kähler-Ricci flow.
result Generalizes Perelman's no local collapsing estimate and provides an analogue of Bishop-Gromov volume comparison for Ricci flow.
The paper examines conditions for Ricci solitons to be Ricci flat or Einstein.
problem Conditions for Ricci solitons to be Ricci flat or Einstein.
method Study of evolution equations of scalar and Ricci curvatures under Ricci flow.
result Conditions for Ricci solitons to be Ricci flat or Einstein.
We introduce a flow of Kähler structures over Fano manifolds with formal limit at infinite time a Kähler-Ricci soliton. This flow correspond to a Perelman's modified backward Kähler-Ricci type flow that we call Soliton-Kähler-Ricci flow. It can be generated by the Soliton-Ricci flow. We assume that the Soliton-Ricci fl…
We consider four extended Ricci flow systems---that is, Ricci flow coupled with other geometric flows---and prove dynamical stability of certain classes of stationary solutions of these flows. The systems include Ricci flow coupled with harmonic map flow (studied abstractly and in the context of Ricci flow on warped pr…
Ricci Flow on Torus Bundlesmath.DG
Study Ricci flow on torus bundles and related manifolds.
problem Compute Ricci flow formulas for torus bundles.
method Use invariant metrics compatible with connections on principal G-bundles.
result Solutions to Ricci flows on Heisenberg groups and Berger 3-spheres.
In this paper, we study the singularities of two extended Ricci flow systems --- connection Ricci flow and Ricci harmonic flow using newly-defined curvature quantities. Specifically, we give the definition of three types of singularities and their corresponding singularity models, and then prove the convergence. In add…
Study the Ricci flow on Finsler surfaces and find solutions.
problem Existence and uniqueness of solutions to the Ricci flow on Finsler surfaces.
method First, study the Finslerian Ricci-DeTurck flow and find a unique short time solution. Then, use this to find a solution to the original Ricci flow.
result Find solutions to the Ricci flow on Finsler surfaces.
The paper examines Ricci flows with closed and smooth tangent flows, proving uniqueness and characterizing ancient flows.
problem Characterizing and understanding Ricci flows with closed and smooth tangent flows.
method Analyzing ancient and finite-time singularity Ricci flows to prove uniqueness and characterizations.
result The tangent flow is unique and characterizes ancient and finite-time singularity flows.
Survey on new Ricci flow techniques.
problem None explicitly stated.
method None explicitly stated.
result None explicitly stated.
Singular Ricci flows Imath.DG
We introduce singular Ricci flows, which are Ricci flow spacetimes subject to certain asymptotic conditions. We consider the behavior of Ricci flow with surgery starting from a fixed initial compact Riemannian 3-manifold, as the surgery parameter varies. We prove that the flow with surgery subconverges to a singular Ri…
Analyzing Ricci Flow on 5D homogeneous manifolds.
problem Understanding Ricci Flow behavior in 5D homogeneous manifolds.
method Applying Ricci Flow to a specific class of 5D homogeneous manifolds.
result Calculations and analysis of Ricci Flow in 5D homogeneous manifolds.
New Ricci flows found with Einstein orbifolds at infinity.
problem Ancient and immortal Ricci flows with Einstein orbifolds at infinity.
method Continuous families of non-isometric ancient Ricci flows and half-PIC ancient flows constructed.
result Found continuous families of non-isometric ancient Ricci flows and half-PIC ancient flows on specific manifolds.
Proves uniqueness of Ricci flow with scaling invariant estimates.
problem Proving uniqueness of Ricci flow with scaling invariant curvature bound.
method Solving Ricci-harmonic map heat flow in unbounded curvature background.
result Complete Ricci flow starting from uniformly non-collapsed, non-negatively curved manifold is unique in dimension three.
Proves analogous result for harmonic Ricci flow, agreeing with gradient Ricci solitons.
problem Consistency of singular points in Ricci flow.
method Developed refined compactness theorems, pseudolocality theorem, and reduced length/volume concept.
result Analogous result for harmonic Ricci flow, agreeing with gradient Ricci solitons.
Almost Hermitian Ricci flowmath.DG
New flow preserves almost Hermitian metrics for manifold study.
problem Curvature flow for almost Hermitian manifolds.
method Introducing a new curvature flow matching Ricci flow and preserving almost Hermitian condition.
result Ricci flow can be used to study almost Hermitian manifolds.
The paper studies mean curvature flow in a Ricci flow background with extended Ricci flow.
problem Analyzing mean curvature flow in a Ricci flow background.
method Computing variational properties and deriving evolution equations for mean curvature and second fundamental form.
result Established a Huisken's monotonicity-type formula for mean curvature solitons in an extended Ricci flow.
Study geometric bounds on generalized Ricci flow.
problem No specific problem stated; focuses on bounds.
method Analogous geometric quantities and bounds proven.
result Geometric and analytic bounds established.
New energy functional bounds Ricci flows on ancient spaces.
problem Bounding Ricci flows on ancient spaces.
method Introducing a dynamical energy functional on compact ancient asymptotically Ricci-flat Ricci flows.
result Provides an upper bound for the ordinary λ-functional.
The Chern-Ricci flowmath.DG
Survey on Chern-Ricci flow for complex manifolds.
problem Understanding and solving open problems in Chern-Ricci flow.
method Parabolic flow of Hermitian metrics on complex manifolds.
result Open problems and new directions in Chern-Ricci flow highlighted.
We characterize the conjugate linearized Ricci flow and the associated backward heat kernel on closed three--manifolds of bounded geometry. We discuss their properties, and introduce the notion of Ricci flow conjugated constraint sets which characterizes a way of Ricci flow averaging metric dependent geometrical data. …
Study weak super Ricci flow through neckpinch in metric measure spaces.
problem Understanding Ricci flow behavior at singularities.
method Introduce weak super Ricci flow and show conditions for continuation.
result Weak super Ricci flow properties at singularities.
Existence and uniqueness theorem for Ricci flow on weighted graphs proved.
problem Existence and uniqueness of solutions to Ricci flow equations on weighted graphs.
method Continuous time normalized Ricci flow approach.
result Existence and uniqueness theorem for solutions to Ricci flow on weighted graphs.
Investigates stability of piecewise flat Ricci flow using analysis and simulations.
problem Stability of piecewise flat Ricci flow.
method Linear stability analysis and numerical simulations.
result Adaptations avoided numerical instability and led to convergence to smooth solutions.
The -Ricci-Yamabe flow exists on closed manifolds.
problem Existence of solutions to the -Ricci-Yamabe flow.
method Showed short time existence and established long time existence theorems.
result Existence of smooth solutions to the -Ricci-Yamabe flow on closed manifolds.
Proves an ε-regularity theorem for Ricci flows, leading to new singularity estimates.
problem Analyzing singularity models in Fano Kähler-Ricci flows.
method Proves ε-regularity theorem and uses it to derive new estimates.
result Establishes new estimates for singularity models of Fano Kähler-Ricci flows.
Study shows Ricci flow's convergence and harmonic map heat flow's long-time existence.
problem Analyzing convergence of Ricci flow and harmonic map heat flow.
method Established long-time existence of harmonic map heat flow between Ricci flow and shrinker.
result Ricci flow converges exponentially to compact integrable shrinkers and at singularities modelled on the shrinker.