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.
The paper studies self-expanding solutions to inverse curvature flows in Euclidean spaces.
problem Investigating self-expanding solutions to inverse curvature flows in Euclidean spaces.
method Using homogeneous symmetric functions of principal curvatures, the paper analyzes self-expanding solutions to a broad class of inverse curvature flows.
result Complete non-compact self-expanders to these flows with asymptotically cylindrical ends must be rotationally symmetric.
Study on positivity in inverse σ-flow convergence for (n-1, n-1) cohomology classes.
problem Finding necessary and sufficient conditions for solvability of inverse σ_k equations.
method Analyzing positivity in the inverse σ_{n-1}-flow for (n-1, n-1) cohomology classes.
result Partial verification of conjecture for inverse σ_{n-1}-flow and 3-folds.
The paper studies a flow of Legendre curves, generalizing the inverse curvature flow of regular curves.
problem Analyzing the inverse curvature flow of Legendre curves.
method Investigates the unique existence, monotonicity, and asymptotic behavior of the flow.
result The flow asymptotically converges to a self-similar solution, categorized by initial curve.
Flow on curves in inversive geometry converges to loxodromics.
problem Gradient flow for curve length in inversive geometry.
method Invariant gradient flow for invariant length functional.
result Solutions exist for all time and converge to loxodromic curves.
Proves existence of proper solutions for inverse mean curvature flow.
problem Existence of proper solutions for inverse mean curvature flow.
method Proves existence theorem assuming non-degeneracy conditions on isoperimetric profile.
result No curvature assumption in existence theorem.
Study inverse curvature flows for capillary hypersurfaces in a unit ball.
problem Understanding the behavior of capillary hypersurfaces under inverse curvature flows.
method Investigate inverse curvature flows for strictly convex, capillary hypersurfaces in the unit Euclidean ball.
result Establish existence and convergence results for inverse curvature flows.
Inverse mean curvature flow converges to a disk in hyperbolic space.
problem Understanding flow behavior in hyperbolic geometry.
method Inverse mean curvature flow with free boundary on geodesic spheres.
result Flow converges to a totally geodesic disk.
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.
Inverse curvature flow studied in anti-de Sitter-Schwarzschild manifold.
problem Analyzing curvature flow in a specific spacetime geometry.
method Inverse hessian quotient curvature flow with star-shaped initial hypersurface.
result The solution exists for all time and converges exponentially fast to the identity.
The round sphere is the only solution to inverse curvature flows under certain conditions.
problem Proving uniqueness of self-conformal solutions to inverse curvature flows.
method Analyzing flows by diffeomorphisms generated by conformal Killing fields.
result The round sphere is the only closed solution to the inverse mean curvature flow and related flows under natural conditions.
New method improves Variational Auto-Encoders using convex combination of Inverse Autoregressive Flows.
problem Improving Variational Auto-Encoders (VAEs) for better performance.
method Introducing multiple lower-triangular matrices with ones on the diagonal and combining them using a convex combination to enrich a linear Inverse Autoregressive Flow.
result The proposed method outperforms other volume-preserving flows and is competitive with state-of-the-art linear normalizing flows.
The paper lists all self-similar solutions for a flow in 2D space.
problem Finding solutions to the inverse mean curvature flow in 2D.
method Obtained a complete list of self-similar solutions.
result Completely enumerated all self-similar solutions for the flow.
Inverse curvature flows in AdS-Schwarzschild manifold converge to a sphere.
problem Understanding the behavior of hypersurfaces in AdS-Schwarzschild geometry.
method Non-parametric inverse curvature flows with 1-homogeneous curvature function.
result Principle curvatures converge to 1 exponentially fast.
Linear flows on inverse limits of tori are defined and it is shown that two linear flows on an inverse limit of tori are equivalent if and only if there is an automorphism of the inverse limit generating the equivalence.
Paper proves stability of quermassintegral inequalities using inverse curvature flow.
problem Stability of quermassintegral inequalities for nearly spherical sets.
method Inverse curvature flow with special rescaling to study quermassintegral inequalities.
result Decreasing rate of k-th quermassintegral is faster than Fraenkel asymmetry for nearly spherical sets.
Paper generalizes Ricci flow for inversive distance circle packings.
problem Deforming circle packings with prescribed cone angles.
method Generalized combinatorial Ricci flow for inversive distance.
result Generalized flow deforms any inversive distance circle packing to a unique packing with prescribed cone angles.
Study of homothetic solitons in inverse mean curvature flow.
problem Understanding the behavior of solitons in inverse mean curvature flow.
method Analyzing solutions that evolve by homotheties of a given submanifold.
result Classification of rotationally invariant Lagrangian homothetic solitons.
The flow converges without Kähler-Einstein and develops ideal sheaves.
problem Analyzing convergence of inverse Monge-Ampere flow without Kähler-Einstein metrics.
method Generalizing the flow and providing conditions for convergence and ideal sheaves development.
result The flow converges without Kähler-Einstein metrics and develops Nadel multiplier ideal sheaves.
The study proves the regularity of inverse mean curvature flow in specific geometric settings.
problem Regularity of inverse mean curvature flow in asymptotically hyperbolic manifolds.
method Utilizing the behavior of Hawking masses, the study shows star-shaped slices after a long time.
result The weak solution of inverse mean curvature flow becomes regular over time.
The paper proves new Minkowski inequalities for flows in warped spaces.
problem Proving new Minkowski inequalities for flows in warped spaces.
method Locally constrained inverse curvature flows in Riemannian warped spaces.
result New Minkowski inequalities are derived for flows in warped spaces.
The paper proves the existence of a hyperbolic inverse mean curvature flow under specific conditions.
problem Proving the existence of a hyperbolic inverse mean curvature flow.
method Short-time existence proof under mean convex and star-shaped initial conditions.
result Short-time existence of hyperbolic inverse mean curvature flow under specified conditions.
Proves higher regularity for anisotropic inverse mean curvature flow.
problem Higher regularity of solutions to anisotropic inverse mean curvature flow.
method Proves Harnack estimate and constructs smooth solutions from C1 initial sets. result Smooth solutions become smooth outside a compact set.
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.
The paper studies how singularities evolve in inverse mean curvature flow.
problem Understanding the evolution of singularities in inverse mean curvature flow.
method Defining a weak solution, analyzing blow-up tangent cones, and proving the evolution of singularities.
result Each singularity is removed when the evolving cone becomes flat, leading to the exact waiting time for a weak solution to be smooth.
Eigenvalues of convex hypersurfaces are bounded by flow.
problem Eigenvalue bounds for convex hypersurfaces.
method Inverse mean curvature flow on convex hypersurfaces.
result Monotonicity of eigenvalues under flow leads to isoperimetric bounds.
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.
New pinching estimates control curvature ratios in inverse curvature flows.
problem Controlling curvature ratios in inverse curvature flows.
method Proving pinching estimates for strictly convex hypersurfaces in space forms.
result Smooth convergence of the inverse curvature flow is proven.
Study inverse mean curvature flow in quaternionic hyperbolic space, proving flow properties and convergence.
problem Evolution of star-shaped hypersurfaces in quaternionic hyperbolic space.
method Inverse mean curvature flow, star-shaped hypersurface, mean convex, convergence analysis.
result Flow is defined for any positive time, evolving hypersurface stays star-shaped and mean convex, induced metric converges to a conformal multiple of the standard sub-Riemannian metric on the sphere.
The paper studies area-preserving and length-preserving inverse curvature flow for planar curves with singularities.
problem Investigating the evolution of planar curves with singularities under area-preserving and length-preserving inverse curvature flow.
method Area-preserving and length-preserving inverse curvature flow for ℓ-convex Legendre curves. result The flow results in a circle for ℓ-convex Legendre curves, providing geometric inequalities. Inverse Mean Curvature Flow bounds star-shaped surfaces' lifetime.
problem Bounding lifetime of star-shaped surfaces under IMCF.
method Derives upper bound on waiting time for variational weak solutions.
result Star-shaped surfaces develop singularities or self-intersections within a prescribed time.
Inverse mean curvature flows studied in warped product manifolds with positive warping factor.
problem Analyzing inverse mean curvature flows in warped product manifolds.
method Investigating starshaped, mean convex hypersurfaces in warped product manifolds with positive warping factor.
result Existence and properties of inverse mean curvature flows in warped product manifolds with positive warping factor.
Flow Annealing Posterior Sampling unifies stochastic-process regression and PDE inverse problems.
problem Function-space posterior sampling for stochastic processes and inverse problems.
method Flow Annealing Posterior Sampling (FAPS) using pretrained function-space flow-matching priors.
result Coherent posterior samples with accurate uncertainty quantification.
Study constructs solutions for evolving hypersurfaces using inverse spacetime mean curvature.
problem Evolution of hypersurfaces in spacetime.
method Weak solutions for hypersurfaces evolving along inverse spacetime mean curvature in asymptotically flat maximal initial data sets.
result Weak solution detects both future- and past-trapped apparent horizons.
New flow expands hypersurfaces in hyperbolic space, showing round limiting shape for certain powers.
problem Understanding the limiting shape of hypersurfaces expanding in hyperbolic space.
method Introduced shifted inverse curvature flow with positive power p for a smooth curvature function. result For 0<p≤1, limiting shape is always round as maximal existence time is approached. Study inverse curvature flows with local constraints in warped manifolds.
problem Understanding geometric flows with local constraints in complex manifolds.
method Inverse curvature flows in warped product manifolds with local constraints.
result Longtime existence and smooth convergence to coordinate slices.
We consider the inverse mean curvature flow in Robertson-Walker spacetimes that satisfy the Einstein equations and have a big crunch singularity and prove that under natural conditions the rescaled inverse mean curvature flow provides a smooth transition from big crunch to big bang. We also construct an example showing…
Study inverse curve shortening flow on hyperbolic plane, classifying solitons.
problem Understanding the behavior of curves in hyperbolic geometry under a specific flow.
method Classifying solitons with respect to vector fields and studying their properties.
result Parabolic solitons are graphs on the y-axis, conformal solitons on the x-axis.
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.
Instead of investigating the Willmore flow for two-dimensional, closed immersed surfaces directly we turn to its inversion. We give a lower bound on the lifespan of this inverse Willmore flow, depending on the concentration of curvature in space and the extension of the initial surface, as well as a characterization of…
The paper proves existence and growth estimates for inverse mean curvature flow and related p-Laplacian Green kernel decay.
problem Existence and growth estimates for inverse mean curvature flow.
method Proving new decay estimates for the Green kernel of the p-Laplacian. result Existence and optimal growth estimates for the weak inverse mean curvature flow.
Investigates conditions for existence of inverse mean curvature flow in warped product manifolds.
problem Ensuring existence of inverse mean curvature flow in warped product manifolds.
method Analyzes sufficient curvature conditions for the Riemannian metric.
result Determines conditions on curvature for flow existence.
Proves uniqueness of geometric flow in various Riemannian manifolds.
problem Proving uniqueness of geometric flow in general Riemannian manifolds.
method Two backward uniqueness theorems for extrinsic geometric flow.
result Backward uniqueness of extrinsic geometric flow in general ambient manifolds.
Rotational symmetry proven for special self-expanders near cylinders.
problem Proving symmetry of self-expanders near cylinders.
method Analyzing self-expanders to inverse mean curvature flow with specific end conditions.
result Proven rotational symmetry for self-expanders with cylindrical ends.
Paper explores stability, regularization, and gradient flows for stochastic inverse problems.
problem Recovering random probability distributions from measurements.
method Direct inversion, variational formulation with regularization, and optimization via gradient flows.
result The choice of metric impacts stability and properties of the optimizer.
Study on curvature flow in Minkowski space for cocompact hypersurfaces.
problem Investigating curvature flow in Minkowski space for cocompact hypersurfaces.
method Investigation of the cocompact inverse \(σ_k\) curvature flow in Minkowski space.
result Longtime existence and convergence of the curvature flow established.
Unified framework reduces NFEs for inverse problems.
problem High computational costs and degraded reconstruction quality in existing LDM-based inverse solvers.
method Consistency Regularised Gradient Flows for posterior sampling and prompt optimization.
result Significantly reduced computational cost with state-of-the-art performance.
In this paper, we first study the behavior of inverse mean curvature flow in Schwarzschild manifold. We show that if the initial hypersurface Σ is strictly mean convex and star-shaped, then the flow hypersurface Σt converges to a large coordinate sphere as t→∞ exponentially. We also describe an a…