Sharp heat kernel estimate on graphs proved.
problem Estimating heat kernels on graphs.
method Proved sharp Davies-Gaffney-Grigor'yan lemma.
result Sharp estimate of heat kernels on graphs.
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48 results for “Davies-Gaffney-Grigor'yan lemma”
We prove a variant of the Davies-Gaffney-Grigor'yan Lemma for the continuous time heat kernel on graphs. We use it together with the Li-Yau inequality to obtain strong heat kernel estimates for graphs satisfying the exponential curvature dimension inequality.
The abstract explores analogues of Hodge theory in Lie algebroids.
problem Exploring analogues of Hodge theory in Lie algebroids.
method Establishing equivalence of conditions and applying algebraic theory to geometric setting.
result Equivalence of analogues of Hodge theory conditions in Lie algebroids.
Paper extends trigonometric summation formula with weights.
problem Trigonometric summation formula by Grigor'yan, Lin and Yau.
method Weighted trigonometric summation formula derivation.
result Extension of trigonometric summation formula.
This is a continuation of Tang and Yan, which investigated the first eigenvalues of minimal isoparametric hypersurfaces with distinct principal curvatures and focal submanifolds in unit spheres. For the focal submanifolds with , the present paper obtains estimates on all the eigenvalues, among others, giving…
Paper improves eigenvalue bounds for Laplacian in Alexandrov spaces.
problem Upper bounds of eigenvalues of Laplacian in subsets.
method Reduces subsets in Chung-Grigor'yan-Yau's inequality for Alexandrov spaces.
result Shows eigenvalue bounds can be achieved with fewer subsets.
Let and let be a complete Riemannian manifold. In a recent work [9], Grigoryan and Sun proved that a pointwise upper bound of volume growth is sufficient for uniqueness of nonnegative solutions of elliptic inequality $$(*)\quad\qquad\qquad\qquad Δu(x)+u^σ(x)\leq 0,\qquad x\in M.\quad\qquad \qquad\q…
A classical result by Alexander Grigor'yan states that on a stochastically complete manifold the non-negative superharmonic -functions are necessarily constant. In this paper we address the question of whether and to what extent the reverse implication holds.
New divergence identity for scalar curvature helps prove rigidity of tensors.
problem Proving rigidity of Codazzi tensors under curvature and invariant conditions.
method Derived a divergence identity for a vector field and applied it to tensor rigidity.
result New proof of Tang-Yan theorem on constant eigenvalues for tensors.
1. Translated by Thomas E. Cecil, Department of Mathematics and Computer Science, College of the Holy Cross, Worcester, MA 01610, USA; E-mail address: cecil@mathcs.holycross.edu 2. Typed by Wenjiao Yan, School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, Beijing Normal University, Beijing 10…
Explains the Schwarz lemma in lecture notes.
problem None explicitly stated; focuses on explanation.
method Expository notes on the Schwarz lemma.
result Explains the Schwarz lemma.
Whitehead's Lemma is a simple result of Stallings folds.
problem None explicitly stated; Whitehead's Lemma is observed as a consequence.
method Observation of Whitehead's Lemma as a consequence of Stallings folds.
result Whitehead's Lemma is a simple result of Stallings folds.
Author provides an alternate proof of the free ribbon lemma.
problem Proving that every free sphere-link in the 4-sphere is a ribbon sphere-link.
method An alternate proof of the free ribbon lemma.
result Provides an alternate proof of the free ribbon lemma.
The paper extends Schwarz's lemma to RC-positivity and complex manifolds.
problem Comparing metrics with RC-positivity in complex manifolds.
method Establishing Schwarz lemmas for RC-positivity and applying them to complex manifolds.
result New diameter and volume comparison theorems.
New CR-structures lemma simplifies CR-manifold deformation proof.
problem Deformation unobstructedness of CR-manifolds.
method New Tian-Todorov lemma applied to CR-manifolds.
result Reproved deformation unobstructedness of CR-manifolds.
Survey on strong closing lemmas in Hamiltonian dynamics.
problem Understanding dynamics in Hamiltonian systems.
method Use spectral invariants in symplectic geometry.
result Proofs of strong closing lemmas in various dimensions.
Paper constructs multivalued harmonic functions on R^3 using twistor methods.
problem Constructing multivalued harmonic functions on R^3.
method Twistor methods to construct multivalued harmonic functions.
result Found a family of multivalued harmonic functions with branching sets as ellipses and quadratic growth at infinity.
Study several weak forms of a lemma on compact complex manifolds.
problem Understanding weak forms of a lemma on compact complex manifolds.
method Complete unified study of weak forms of the $\ddb-$Lemma.
result Unified understanding of various weak forms of the $\ddb-$Lemma.
Unified Schwarz lemma in Kähler and Hermitian geometry.
problem Various forms of the Schwarz lemma in Kähler and Hermitian geometry.
method Introducing new curvatures to refine and elucidate the real bisectional curvature.
result Unified Chern-Lu, Aubin-Yau, and Chen-Cheng-Look Schwarz lemmas.
Paper generalizes Schwarz Lemma for VT harmonic maps with conditions.
problem Generalizing Schwarz Lemma for a specific type of harmonic maps.
method Conditions on eigenvalues and Ricci curvature are used to prove the lemma.
result Schwarz Lemma for VT harmonic maps proved with distance and volume decreasing properties.
Formulates Index III lemma and Rauch III theorem with applications.
problem Develops new mathematical theorems based on existing ones.
method Formulation of Index III lemma and Rauch III theorem based on Index I, II lemmas and Rauch I, II theorems.
result Presented Rauch's type theorem and volume comparison result as applications.
New Schwarz Lemma for Bergman metrics in bounded domains.
problem Finding bounds for Bergman metrics in bounded domains.
method Using Cauchy-Schwarz inequality from probability theory.
result Established a new Schwarz Lemma for Bergman metrics.
Selberg's Lemma fails for certain curved manifolds.
problem Applying Selberg's Lemma to negatively curved Hadamard manifolds.
method Proving the failure of Selberg's Lemma for specific groups of manifolds.
result Selberg's Lemma does not hold for discrete isometry groups of negatively curved Hadamard manifolds.
Tucker and Ky Fan's lemma are combinatorial analogs of the Borsuk-Ulam theorem (BUT). In 1996, Yu. A. Shashkin proved a version of Fan's lemma, which is a combinatorial analog of the odd mapping theorem (OMT). We consider generalizations of these lemmas for BUT-manifolds, i.e. for manifolds that satisfy BUT. Proofs rel…
Boundary Value Problem and Discrete Schwarz-Pick Lemma for Generalized Hyperbolic Circle Packingsmath.DG
Paper proves a discrete Schwarz-Pick lemma for generalized circle packings.
problem Comparing geometric quantities of circle packings with different boundary values.
method Combinatorial Calabi flows and maximum principle.
result Discrete Schwarz-Pick lemma proven for generalized circle packings.
The paper improves Zakalyukin's lemma for frontals and applies it to surface singularities.
problem Improving the conditions under which wave front germs imply map germs.
method Generalization of Zakalyukin's lemma for frontals and applications to surface singularities.
result The paper provides a more general version of Zakalyukin's lemma for map germs.
Paper proves almost Schur Lemma on smooth metric measure spaces.
problem Proving a specific lemma on metric measure spaces.
method Proves almost Schur Lemma using closed smooth metric measure spaces.
result Implications of the lemma for X. Cheng's and De Lellis-Topping's results.
Meridian lemma extended to fully alternating links in thickened surfaces.
problem Extending Menasco's meridian lemma to fully alternating links in thickened surfaces.
method Developed a new meridian lemma for fully alternating links in thickened orientable surfaces of positive genus.
result The meridian lemma holds for fully alternating links in thickened surfaces.
A quantitative closing Lemma and Partner orbits on Riemannian manifolds with negative curvaturemath.DG
Proves a quantitative closing lemma for negatively curved manifolds.
problem Closing lemma for negatively curved manifolds.
method Quantitative closing lemma proof.
result Study of partner and pseudo-partner orbits for self-crossing closed geodesics.
Based on ideas of Pigolla and Setti \cite{PS} we prove that immersed submanifolds with bounded mean curvature of Cartan-Hadamard manifolds are Feller. We also consider Riemannian submersions with compact minimal fibers, and based on various criteria for parabolicity and stochastic completeness, see \c…
Paper generalizes Schwarz lemma for harmonic maps between Riemannian manifolds.
problem Generalizing Schwarz lemma for harmonic maps.
method Using Bochner techniques and sub-Laplacian comparison theorem.
result Established a generalization of Schwarz lemma for transversally harmonic maps.
Margulis Lemma on spacesmath.DG
Extends Margulis Lemma to RCD(K,N) spaces.
problem Applying Margulis Lemma to new geometric structures.
method Improved Regularity Estimates for Regular Langrangian Flows.
result Margulis Lemma extended to RCD(K,N) spaces.
Study joins and intersections of subgroups in free groups, disproving and repairing a lemma.
problem Disproving and repairing a lemma on joins and intersections of subgroups in free groups.
method Analyzing graphs of joins and intersections of finitely generated subgroups of a free group.
result Showed how to disprove and repair a lemma of Imrich and Müller on these graphs.
Proves Poincaré lemma on specific sub-Riemannian structures.
problem Solving an open problem on Poincaré lemma for corank 1 sub-Riemannian structures.
method Combines Poincaré lemma on Riemannian manifolds with a path integral formula.
result Necessary and sufficient 'curl-vanishing' conditions for Poincaré lemma.
Corrects a lemma in a 2009 paper about contact homology and Floer homology.
problem An error in a lemma about contact homology and Floer homology.
method None, as it is a correction of an existing lemma.
result Corrects an error in a previously published lemma.
The paper characterizes when the -lemma holds for twistor spaces.
problem Characterizing the -lemma for twistor spaces.
method Study Bott-Chern and Aeppli cohomologies of twistor spaces.
result Explicit computation of Dolbeault cohomology for flat torus twistor space.
New Morse lemma handles functions going to negative infinity.
problem Deforming functions with negative infinity behavior.
method Generalized Morse Theory lemma for functions going to negative infinity.
result Valid for functions with suitable growth condition.
For a symplectic manifold , not necessarily hard Lefschetz, we prove a version of the Merkulov --lemma. We also study the --lemma and related cohomologies for compact symplectic solvmanifolds.
Positive representations on surfaces have positive cross-ratios and satisfy a collar lemma.
problem Characterizing representations of surface groups with positive properties.
method Proving a collar lemma and showing positivity of cross-ratios for -positive representations.
result Closed subsets of representation varieties are characterized by -positive representations.
Proves a generalized Whitehead cut vertex lemma for tree groups.
problem Extending Whitehead's cut vertex lemma to tree group conjugacy classes.
method Proves a version of Whitehead's lemma for tree groups.
result Establishes a cut vertex in star graphs for tree group conjugacy classes.
Proves a general ∂∂̄-lemma and applies it to a Fujino conjecture.
problem Establishing a general ∂∂̄-lemma and its applications.
method Develops a general ∂∂̄-lemma and applies it to Fujino's conjecture.
result Establishes a Kähler version of Fujino's injectivity theorem.
Enhanced Schwarz lemma for Hermitian manifolds with new curvature constraints.
problem Improving Schwarz lemma for holomorphic maps between Hermitian manifolds.
method Introducing new curvature constraints on source and target manifolds, controlling by holomorphic sectional curvature.
result Significant improvements on the Wu--Yau theorem and Schwarz lemma for Gauduchon connections.
Corrects a proof gap in the Morse lemma for hyperbolic spaces.
problem Gap in the proof of optimal bounds for the Morse lemma in Gromov-hyperbolic spaces.
method Describes a computer certification of the corrected result.
result Corrects the main theorem of [ShCh13a] in optimal bounds for the Morse lemma.
Schwarz lemma extended to equality cases and curvature on manifolds.
problem Extending Schwarz lemma to equality cases and studying curvature.
method Analyzing Schwarz lemma inequalities and equalities, studying holomorphic sectional curvature.
result Holomorphic maps are totally geodesic and have constant rank when Schwarz lemma equality holds.
Generalized Stacey-Roberts lemma for Banach manifolds.
problem Constructing Lie groupoids of smooth mappings in infinite-dimensional geometry.
method Generalization of the Stacey-Roberts lemma to Banach manifolds with smooth partitions of unity.
result Remedied an error in the original proof for finite-dimensional setting.
Generalizes Schwarz lemma for conical Kähler metrics with arbitrary cone angles.
problem Applying Schwarz lemma to conical Kähler metrics with general cone angles.
method Using a barrier function and maximum principle argument, extending to arbitrary cone angles.
result Generalized Schwarz lemma to conical Kähler metrics with arbitrary cone angles.
Thurston's jigglingmath.GT
Thurston's jiggling lemma simplifies triangulations.
problem Simplifying triangulations into a general position.
method Alternative, conceptual proof and generalization to manifolds.
result A more straightforward proof of Thurston's jiggling lemma.
Extends Stein's lemma to exponential-family mixtures for gradient computation.
problem Computing gradients for complex distributions with weak assumptions.
method Generalizes Stein's lemma to exponential-family mixtures and applies it to reparameterization trick.
result Derives new gradient identities for various distributions.