Study inverse problems for twisted geodesic flows on manifolds.
problem Understanding inverse problems for twisted geodesic flows.
method Generalized ray transforms and tensor tomography.
result New insights into rigidity problems for twisted geodesic flows.
Solves curve migration problem with elastic flows.
problem Curve migration problem with natural boundary conditions.
method Constructing migrating elastic flows.
result Extends previous work to purely local flow.
Study on translating mean curvature flow and its Dirichlet problem.
problem Understanding translating solitons and their properties.
method Developed a new evolving geometric flow called translating mean curvature flow.
result Global existence and convergence of the flow for the Dirichlet problem.
New flow method solves Christoffel-Minkowski problem.
problem Solving Christoffel-Minkowski problem.
method Entropy preserving curvature flow with global term.
result Entropy preserving flow solves Christoffel-Minkowski problem.
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.
Paper solves Orlicz-Aleksandrov problem using Gauss curvature flow.
problem Orlicz-Aleksandrov problem
method Gauss curvature flow
result Existence of smooth solutions
Study solves a generalized Christoffel-Minkowski problem using curvature flow.
problem Generalization of the Lp-Christoffel-Minkowski problem. method Anisotropic curvature flow to derive long-time existence and smooth solutions.
result Existence of smooth solutions for c=1 under certain initial data. Bayesian optical flow estimates motion with uncertainty quantification.
problem Ill-posed inverse problem of optical flow.
method Statistical approach treating optical flow as a statistical inverse problem.
result Bayesian optical flow provides statistical estimates of motion and uncertainty.
Flow proposed to solve Chern-Yamabe problem, showing it's an Euler-Lagrange equation of a functional.
problem Chern-Yamabe problem in differential geometry.
method Flow approach to study the problem, showing it's an Euler-Lagrange equation of a functional.
result Monotonicity of the functional along the flow, but not bounded from below.
New method solves a generalized Minkowski problem using a curvature flow.
problem Generalized Minkowski problem for smooth measures.
method Flow involving Gauss curvature and support function.
result Existence of solutions for the dual Orlicz-Minkowski problem.
Study of a flow related to the Orlicz-Minkowski problem for convex hypersurfaces.
problem Orlicz-Minkowski problem involving Gauss curvature and support function.
method Generalized Gauss curvature flow for convex hypersurfaces in Euclidean n-space.
result Long-time existence and convergence of the flow, leading to existence results for the Orlicz-Minkowski problem.
Study on convergence rate of weighted Yamabe flow.
problem Weighted Yamabe problem on smooth metric measure spaces.
method Weighted Yamabe flow and its convergence rate analysis.
result Study and analysis of convergence rate of the weighted Yamabe flow.
Study flows for capillary Minkowski problems in half-spaces.
problem Existence and behavior of capillary Minkowski problems.
method Anisotropic capillary Gauss curvature flows.
result Long-time existence and asymptotic behavior of flows.
Study an anisotropic capillary flow to solve capillary Orlicz-Minkowski problem.
problem Solve capillary Orlicz-Minkowski problem without evenness assumption.
method Analyze an anisotropic capillary Gauss curvature flow to prove convergence and establish existence.
result Establish existence result for capillary Orlicz-Minkowski problem without evenness assumption.
Study preserves volume in warped spaces, solves isoperimetric problem.
problem Isoperimetric problem in warped product spaces.
method Normalized hypersurface flow in warped product spaces.
result Solves isoperimetric problem for specific domains.
A method for estimating signal distributions from inverse problems using normalizing flows.
problem Estimating the distribution of the underlying signal from observations in inverse problems.
method A framework for approximate inference on a pre-trained unconditional flow model, using a composition of two flow models for stable variational inference.
result Our method produces high-quality samples with uncertainty quantification and can be amortized for zero-shot inference.
Geometrically solves Schrödinger flow on sphere.
problem Solving periodic Cauchy problem for Schrödinger flow on sphere.
method Explicit geometric algorithm for construction of solutions.
result Explicit geometric algorithm for solving Schrödinger flow on sphere.
Paper solves Musielak-Orlicz-Gauss image problem using parabolic flows.
problem Characterize Musielak-Orlicz-Gauss image measure of convex bodies.
method Study of parabolic flows and approximation technique.
result Provides solutions to the extended Musielak-Orlicz-Gauss image problem.
CoSMIC extends flow-based SVI to transdimensional problems.
problem Bayesian structure learning and model selection with multi-model parameter spaces.
method Normalizing flows with a combined stochastic variational transdimensional inference approach.
result Improved performance on high-cardinality model spaces.
We solve image inverse problems using a flow-based noise model.
problem Image inverse problems with complex noise patterns.
method Normalizing flow prior for maximum a posteriori estimation.
result Empirical validation on various inverse problems.
Gradient flow solves curvature problem on surfaces with conical points.
problem Solving curvature problems on surfaces with conical points.
method Introduced and analyzed a gradient flow on closed Riemann surfaces with conical singularities.
result Gradient flow proves long-time existence and convergence under certain assumptions.
Let us consider a projective manifold and Ω a volume form. We define the gradient flow associated to the problem of Ω-balanced metrics in the quantum formalism, the Ω−balacingflow.Atthelimitofthequantization,weprovethattheΩ−balacingflowconvergestowardsanaturalflowinKa¨hlergeometry,theΩ$-Kä…
New method solves generalized Minkowski problem for torsional rigidity.
problem Generalized Minkowski problem for torsional rigidity.
method Flow method
result Existence of solutions for general measures.
A new method for reconstructing flows from perturbed distributions.
problem Reconstructing flows from perturbed probability distributions.
method Integrable vector fields and Green's functions.
result A nonparametric flow can be computed to generate samples from a perturbed distribution.
Surveying problems with positive curvature forms, focusing on Ricci flow.
problem Problems with Riemannian manifolds and positive curvature forms.
method Explains how recent Ricci flow theory can solve these problems.
result Ricci flow is well-suited for solving problems involving positive curvature.
Investigate scalar curvature under geometric flows
problem Behavior of scalar curvature under geometric flows
method Three specific cases: Ricci flow, Kähler-Ricci flow, Laplacian flow
result Long-time existence of flows
Study anisotropic flows solving Orlicz-Minkowski problems, proving existence and new results.
problem Anisotropic non-homogeneous Gauss curvature flows and Orlicz-Minkowski problems.
method Long-time existence and behavior analysis, parabolic approximation method, curvature flow.
result Existence and new results for Orlicz-Minkowski problems, including Lp versions. A paper uses RL to design microfluidic flow shapes efficiently.
problem Designing complex flow shapes in microfluidics using inverse problems.
method Formulated as a Reinforcement Learning (RL) problem, trained a DoubleDQN agent.
result Success frequency reached 90% in 200,000 episodes, rewards converged.
New flow deforms Riemannian metrics smoothly.
problem Deforming Riemannian metrics on spin manifolds.
method Parabolic flow based on Dirac-Einstein functional.
result Local well-posedness of smooth solutions proved.
Study on migrating elastic flows of curves across half-planes.
problem Migrating elastic flows of curves from upper to lower half-planes.
method Analytical and numerical construction of migrating elastic flows.
result Construction of various migrating elastic flows.
Paper resolves spherical curvature flow problem.
problem Existence of ideal circle patterns in spherical background geometry.
method Introduces a combinatorial geodesic curvature flow in spherical background geometry.
result Characterizes sufficient and necessary conditions for flow convergence.
New method uses diffusion models to solve inverse problems.
problem Solving ill-posed inverse problems with powerful priors.
method Formulate posterior sampling as a regularized Wasserstein gradient flow in latent space.
result Demonstrates improved performance on standard benchmarks.
The paper solves curvature problems on graphs using a special flow.
problem Solving curvature problems on finite graphs.
method Defined the Calabi flow for a specific curvature type and established its global existence and convergence.
result The solution to the Calabi flow exists globally and converges under certain conditions.
Flow deforms curves to match an embedded target.
problem Evolve curves to match an embedded target curve.
method Target flow with curve shortening and forcing term.
result Smooth convergence to the target curve.
Efficiently solves inverse problems with diffusion and flow models in just a few steps.
problem Solving inverse problems like super-resolution, inpainting, or deblurring using diffusion or flow models.
method Conditional Conjugate Integrators framework that projects inverse problem dynamics into a more amenable space for sampling.
result Generates high-quality samples in as few as 5 conditional sampling steps, outperforming competing methods.
Identifies a gradient flow to solve kernel learning problems with noise reduction.
problem Kernel learning problem with Gaussian noise.
method Riemannian gradient flow with continuous Lyapunov functionals.
result Flow reduces noise and finds stationary points.
Continues study on special Lagrangian graphs and flow solutions.
problem Long time existence and convergence of a class of fully nonlinear flows.
method Analyzes special Lagrangian graphs with prescribed second boundary conditions.
result Long time existence and convergence for a family of special Lagrangian graphs.
Study anisotropic inverse Gauss curvature flows and solve dual Orlicz Minkowski problems.
problem Solving dual Orlicz Minkowski problems for anisotropic flows.
method Anisotropic inverse Gauss curvature flows and stationary solutions.
result New existence results for dual Orlicz Minkowski problems for smooth measures.
Study on fractional curvature flow on unit sphere, extending previous work.
problem Fractional Nirenberg problem on unit sphere.
method Fractional conformal curvature flow on unit sphere.
result Perturbation result for fractional Nirenberg problem with σ∈(1/2,1). Study of mean curvature flow with obstacles using singular perturbation.
problem Obstacle problem associated to mean curvature flow.
method Geometric vanishing-viscosity approximation with singular perturbation.
result Generic level sets are distributional solutions of the obstacle problem.
The paper solves a generalized Christoffel-Minkowski problem using a curvature flow.
problem Solving the (p,q)-Christoffel-Minkowski problem.
method Investigating the problem via an expanding curvature flow.
result Existence and uniqueness of smooth solutions to the (p,q)-Christoffel-Minkowski problem.
Study on geodesic flows on a two-torus for additional first integrals.
problem Existence of additional first integrals for geodesic flows on a two-torus.
method Analyzes polynomial and quadratic first integrals, relates to soliton equations.
result Nonexistence of an additional quadratic first integral for certain magnetic geodesic flows.
The paper solves curvature problems on infinite hyperbolic surfaces.
problem Prescribed curvature flow on hyperbolic surfaces with infinite topological type.
method Introduced a prescribed curvature flow adapted to infinite cellular decompositions.
result Established well-posedness of the flow and proved convergence under certain conditions.
Flow approach solves Ricci equation boundary problem.
problem Solving generalized Loewner-Nirenberg problem for σk-Ricci equation. method Flow approach to prove existence and uniqueness of solution.
result Solution converges to the boundary value as time goes to infinity.
Paper studies inverse curvature flows and solves related geometric problems.
problem Inverse curvature flows and related geometric problems.
method Analyzes a class of expanding flows with specific speeds and proves existence and convergence.
result Proves the existence and convergence of flows under certain conditions, leading to new solutions to geometric problems.
Variational approximations for curve flows on Riemannian manifolds.
problem Approximating solutions to curvature and elastic flow problems on Riemannian manifolds.
method Variational formulations, finite element approximations, piecewise linear elements, stability analysis.
result Derived schemes can compute rotationally symmetric self-shrinkers and geodesics.
Cascading flows improve variational inference in structured programs.
problem Challenges in variational inference for complex probabilistic programs.
method Integrates normalizing flows and ASVI to create cascading flows, which embed the forward-pass of probabilistic programs.
result Cascading flows outperform normalizing flows and ASVI in structured inference problems.
Modified flow smooths conical Kähler-Ricci problem.
problem Smooth approximation of modified conical Kähler-Ricci flow.
method Constructing a long-time solution of the modified conical Kähler-Ricci flow as the limit of a sequence of smooth Kähler-Ricci flows.
result Long-time solution of the modified conical Kähler-Ricci flow.