We study Riemannian manifolds with boundary under a lower Bakry-E'mery Ricci curvature bound. In our weighted setting, we prove several rigidity theorems for such manifolds with boundary. We conclude a rigidity theorem for the inscribed radii, a volume growth rigidity theorem for the metric neighborhoods of the boundar…
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,341 papers · 148 categories
Trend · papers per month
48 results for “Bakry-Émery Ricci”
The paper generalizes a curvature result for hyperbolic affine hyperspheres.
problem Curvature properties of hyperbolic affine hyperspheres.
method Tensorial maximum principle applied to the Bakry-Émery tensor.
result Metric measure spaces have non-positive Bakry-Émery tensor.
Gradient estimates for special harmonic functions on manifolds.
problem Estimating gradients of -harmonic functions on Riemannian manifolds.
method Using Moser iteration method, volume comparison theorem, and Sobolev embedding theorem.
result Explicit global gradient estimates for positive entire -harmonic functions.
Local existence and uniqueness of Bakry-Émery Ricci flow solutions on finite graphs.
problem Analyzing the behavior of Ricci flow on finite graphs.
method Local existence and uniqueness proof for solutions of the Bakry-Émery Ricci flow.
result Local existence and uniqueness of solutions to the Ricci flow on finite graphs.
The paper extends topological results to noncompact spaces with nonnegative N-Bakry Émery Ricci curvature.
problem Generalizing topological results to noncompact spaces with nonnegative N-Bakry Émery Ricci curvature.
method Study of the Splitting Theorem and geodesic loops to infinity property in relation to spaces with nonnegative N-Bakry Émery Ricci curvature.
result If is a complete, noncompact Riemannian manifold with nonnegative N-Bakry Émery Ricci curvature where , then is 0.
The paper extends Bonnet-Myers theorems using Bakry-Emery Ricci curvature.
problem Proving extensions of Bonnet-Myers theorems with a new curvature measure.
method Using Bakry-Emery Ricci curvature to extend Bonnet-Myers theorems.
result Proves extensions of Bonnet-Myers theorems.
Proves volume comparison and monotonicity for Bakry-Émery Ricci curvature.
problem Volume comparison and monotonicity for Bakry-Émery Ricci curvature.
method Relative volume comparison theorem for -bound of Bakry-Émery Ricci curvature and gradient of potential function.
result Modified proof for volume comparison and monotonicity of Kähler-Ricci flow.
Study improves comparison geometry for spaces with Bakry-Émery Ricci tensor bounds.
problem Improving comparison geometry for spaces with specific Ricci tensor bounds.
method Proved mean curvature and volume comparison estimates on smooth metric measure spaces.
result Generalized diameter, eigenvalue, and volume growth estimates.
The paper proves a compactness theorem for spaces with Bakry-Emery Ricci tensor.
problem Compactness in spaces with Bakry-Emery Ricci tensor.
method Proving -mean curvature comparison and defining a Myers-type compactness theorem.
result Improves a result from Soylu by using a weaker condition on .
The Bakry-Émery-Ricci tensor is extended and comparison theorems are proven.
problem Extending the Bakry-Émery-Ricci tensor and proving comparison theorems.
method Generalizations of the drifted Laplacian and Bakry-Émery-Ricci tensor, mean curvature comparison theorem, Myers-type theorem, Cheeger-Gromoll splitting theorem.
result Proved a version of the mean curvature comparison theorem and its consequences.
Derives gradient bounds for f-heat equations on manifolds with Bakry-Emery Ricci curvature.
problem Gradient estimates for positive solutions of f-heat equations on manifolds with specific curvature conditions.
method Applies Li-Yau gradient estimates to positive solutions of the f-heat equation on closed manifolds with Bakry-Emery Ricci curvature bounded below.
result Derives Li-Yau gradient bounds for positive solutions of the f-heat equation.
The paper proves inequalities under Bakry-Émery-Ricci curvature bounds.
problem Proving functional inequalities under lower Bakry-Émery-Ricci curvature bounds.
method Lower -Bakry-Émery-Ricci curvature bounds with -range.
result Proves Cheng type inequality and local Sobolev inequality.
The Bakry-Emery tensor gives an analog of the Ricci tensor for a Riemannian manifold with a smooth measure. We show that some of the topological consequences of having a positive or nonnegative Ricci tensor are also valid for the Bakry-Emery tensor. We show that the Bakry-Emery tensor is nondecreasing under a Riemannia…
The paper proves geometric comparisons on metric measure spaces with integral Bakry-Émery Ricci tensor bounds.
problem Geometric comparisons on metric measure spaces with specific tensor bounds.
method Integral radial Bakry-Émery Ricci tensor bounds and potential function/gradient bounds.
result Diameter and eigenvalue estimates on smooth metric measure spaces.
Proves Sobolev inequality on manifolds with specific curvature properties.
problem Proving Sobolev inequality on manifolds with asymptotically nonnegative Bakry-Émery Ricci curvature.
method Density and Bakry-Émery Ricci curvature.
result Proves Sobolev inequality on manifolds with asymptotically nonnegative Bakry-Émery Ricci curvature.
Extends a result on manifolds with specific curvature properties.
problem Extending a result on manifolds with nonnegative Bakry-Émery Ricci curvature.
method Extends a recent result by S. Brendle to manifolds with densities and nonnegative Bakry-Émery Ricci curvature.
result Extends a result on manifolds with specific curvature properties.
Study preserves metrics with positive Bakry-Émry Ricci curvature via surgery.
problem Preserving metrics with positive Bakry-Émry Ricci curvature after surgery.
method Established theorems for connected sums and surgeries along higher-dimensional spheres.
result Local surgery results for positive Bakry-Émry Ricci curvature.
Study compares spectral properties of a specific tensor in geometry.
problem Comparing spectral properties of a specific tensor in geometry.
method Diameter and global weighted volume comparison with a positive lower bound on the -Bakry-Emery Ricci tensor.
result Established diameter and volume comparisons for tensors with positive lower bounds.
The paper proves Laplacian comparison theorems for modified m-Bakry-Emery Ricci tensors on Riemannian manifolds.
problem Analyzing modified m-Bakry-Emery Ricci tensors on Riemannian manifolds.
method Proving Laplacian comparison theorems using modified m-Bakry-Emery Ricci tensors under m≤1.
result Optimal conditions for modified m-Bakry-Emery Ricci tensors under m≤1 are derived.
In this paper, we study stable weighted minimal hypersurfaces in manifolds with nonnegative Bakry-Emery Ricci curvature. We will give some geometric and topological applications. In particular, we give some partial classification of complete 3-manifolds with nonnegative Bakry-Emery Ricci curvature assuming that is …
New diameter estimate on manifolds with positive Bakry-Émery Ricci tensor.
problem Estimating the diameter of manifolds with specific curvature conditions.
method Using generalized mean curvature comparison on excess function.
result Sharper diameter estimate than previous results.
In this paper we derive Cheng-Yau, Li-Yau, Hamilton estimates for Riemannian manifolds with Bakry-Emery Ricci curvature bounded from below, and also global and local upper bounds, in terms of Bakry-Emery Ricci curvature, for the Hessian of positive and bounded solutions of the weighted heat equation on a closed Riemann…
In this paper we study some splitting properties on complete noncompact manifolds with smooth measures when -dimensional Bakry-Émery Ricci curvature is bounded from below by some negative constant and spectrum of the weighted Laplacian has a positive lower bound. These results extend the cases of Ricci curvatur…
The study proves a compactness theorem for manifolds with specific curvature conditions.
problem Proving compactness theorems for manifolds with Bakry-Emery Ricci tensor.
method Using Bakry-Emery Ricci tensor and smooth measure.
result Generalized Myers compactness theorem proved.
Eigenvalue estimates for Beltrami-Laplacian under specific curvature conditions.
problem Estimating eigenvalues of the Beltrami-Laplacian on manifolds with Bakry-Émery Ricci curvature.
method Using Bakry-Émery Ricci curvature conditions, the paper derives lower bounds for eigenvalues of the Beltrami-Laplacian.
result Lower bounds for eigenvalues of the Beltrami-Laplacian depend on curvature, gradient bounds, dimension, and diameter of the manifold.
Develops framework for Bakry-Emery estimate on Dirichlet spaces.
problem Lack of Ricci curvature lower bounds in metric graphs.
method General framework on Dirichlet spaces for weak Bakry-Emery estimate.
result Establishes estimate in metric graphs where traditional curvature bounds are not applicable.
The study bounds heat kernel for manifolds with specific curvature conditions.
problem Estimating heat kernel for manifolds with Bakry-Émery Ricci curvature.
method Gaussian upper bound for heat kernel, proving L^1-Liouville property, deriving eigenvalue bounds.
result Established Gaussian upper bound for heat kernel, derived eigenvalue bounds.
The paper characterizes upper bounds of Bakry-Emery curvature.
problem Characterizing upper bounds of Bakry-Emery curvature on Riemannian manifolds.
method Using functional inequalities on path space.
result Characterizations for upper bounds of Bakry-Emery curvature are provided.
We study some function-theoretic properties on a complete smooth metric measure space with Bakry-Émery Ricci curvature bounded from below. We derive a Moser's parabolic Harnack inequality for the -heat equation, which leads to upper and lower Gaussian bounds on the -heat kernel. We also prove $L^…
In this paper, we prove two generalized versions of the Cheeger-Gromoll splitting theorem via the non-negativity of the Bakry-Émery Ricci curavture on complete Riemannian manifolds.
Comparison theorems in centro-affine differential geometry
problem rigidity phenomena of comparison theorems
method study of centro-affine differential geometry
result examples of rigidity phenomena
In this paper, we first prove a compactness theorem for the space of closed embedded -minimal surfaces of fixed topology in a closed three-manifold with positive Bakry-Émery Ricci curvature. Then we give a Lichnerowicz type lower bound of the first eigenvalue of the -Laplacian on compact manifold with positive $m…
Motivated and inspired by the recent work of Colding [5] and Colding-Minicozzi [6] we derive several families of monotonicity formulas for manifolds with nonnegative Bakry-Emery Ricci curvature, extending the formulas in [5, 6].
We first extend Cheeger-Colding Almost Splitting Theorem to smooth metric measure spaces. Arguments utilizing this extension of the Almost Splitting Theorem show that if a smooth metric measure space has almost nonnegative Bakry-Emery Ricci curvature and a lower bound on volume, then its fundamental group is almost abe…
For Riemannian manifolds with a measure we prove mean curvature and volume comparison results when the -Bakry-Emery Ricci tensor is bounded from below and is bounded or is bounded from below, generalizing the classical ones (i.e. when is constant). This leads to ext…
Analyticity of heat equation extended to Bakry-Émery Ricci curvature manifolds.
problem Analyticity of solutions to heat equation under specific curvature conditions.
method Analyzes analyticity in time for smooth solutions on Riemannian manifolds with Bakry-Émery Ricci curvature.
result Analyticity extended to all gradient Ricci solitons and certain spaces.
Graphs with Bakry-Emery curvature have bounded diameter.
problem Bounding the diameter of graphs with positive Ricci curvature.
method Proving diameter bounds using Bakry-Emery curvature and vertex degree.
result First Bonnet-Myers type theorem for unbounded graph Laplacians.
Gradient estimates, Bakry-Emery Ricci curvature and ellipticity for unbounded graph Laplaciansmath.DG
Gradient estimates for unbounded graph Laplacians under Bakry-Emery curvature.
problem Gradient estimates for unbounded graph Laplacians.
method Proving gradient estimates under Bakry-Emery curvature bounds for unbounded graph Laplacians with ellipticity assumption.
result Gradient estimates and applications to completeness and finiteness of stochastically complete graphs.
Classifies graphs with Bonnet-Myers sharp curvature and connects it to Bakry-Émery curvature.
problem Classifying graphs with specific curvature properties.
method Introducing Bonnet-Myers and Lichnerowicz sharpness in Ollivier Ricci curvature, combinatorial reformulation, and relating to Bakry-Émery curvature.
result Classification of graphs including hypercubes, cocktail party graphs, and Johnson graphs .
The paper explores curvatures on graphs and their implications for Ricci flatness.
problem Comparing and understanding different curvature notions on graphs and their implications for Ricci flatness.
method Analyzing Ollivier Ricci curvature and Bakry-Émery curvature on combinatorial graphs, investigating graph products, and proving curvature properties.
result Non-negativity of Ollivier Ricci curvature implies non-negativity of Bakry-Émery curvature under specific conditions.
Scalar-tensor gravitation theories, such as the Brans-Dicke family of theories, are commonly partly described by a modified Einstein equation in which the Ricci tensor is replaced by the Bakry-Émery-Ricci tensor of a Lorentzian metric and scalar field. In physics this formulation is sometimes referred to as the "Jordan…
Nearly spherical, positively curved surfaces are mapped from a sphere.
problem Mapping nearly spherical, positively curved surfaces from a sphere.
method Combines Ricci flow, Kim-Milman construction, and Bakry-Émery criterion.
result Every nearly spherical, positively curved surface is the contractive image of a round sphere.
The study introduces a new curvature concept for weighted graphs and applies it to warped products.
problem Establishing curvature bounds for doubly warped product graphs.
method Developed a new notion of curvature for weighted graphs and applied it to warped products, establishing bounds in terms of constituent graph curvatures.
result Established curvature bounds for $\left(R_1,R_2
ight)$-doubly warped products of smooth measure spaces.
New volume comparison theorem for gradient Ricci almost solitons.
problem Volume comparison and rigidity of gradient Ricci almost solitons.
method Established a new volume comparison theorem with Bakry-Emery Ricci curvature.
result New volume rigidity result for gradient Ricci almost solitons.
Paper proves new theorems about curvature in weighted manifolds.
problem Understanding curvature in weighted manifolds.
method Proved spectral comparison and splitting theorems for infinity-Bakry-Emery Ricci curvature.
result Results extend existing theorems and provide new supplements.
We compute first variation formulas for the complex components of the Bakry-Emery-Ricci endomorphism along Kähler structures. Our formulas show that the principal parts of the variations are quite standard complex differential operators with particular symmetry properties on the complex decomposition of the variation o…
Eigenvalue estimates without Bakry-Emery-Ricci bounds established.
problem Eigenvalue estimates for Laplace-Beltrami operators with drift.
method Establishes a lower bound for real eigenvalues without assuming self-adjointness or additional regularity of the drift.
result Establishes a lower bound on the spectrum of Laplace-Beltrami operators without assuming a lower bound for the Bakry-Emery Ricci tensor.
The study bounds harmonic radius for manifolds with Bakry-Émery Ricci curvature.
problem Bounding harmonic radius for manifolds with Bakry-Émery Ricci curvature.
method Lower bound using harmonic radius, Green's function argument, and linear algebra.
result Extended Codimension 4 Theorem to manifolds with Bakry-Émery Ricci curvature.