New proof that certain stable surfaces can't have genus 1.
problem Characterizing stable constant mean curvature surfaces with free boundary.
method Modified Hersch type balancing argument.
result Proves that surfaces cannot have genus 1.
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 “Hersch type balancing argument”
Upper bounds for second Robin eigenvalue on Riemannian surfaces.
problem Bounding the second Robin eigenvalue of Schrödinger operators on Riemannian surfaces.
method Geometric upper bound via Hersch balancing argument on capped surfaces.
result Sharp geometric restrictions for minimal surfaces in negatively curved manifolds.
The study improves stability conditions for CMC hypersurfaces with free boundary in a ball.
problem Stability conditions for CMC hypersurfaces with free boundary in a ball.
method Analyzes inequalities involving length, area, and mean curvature; uses stability lemma and results from A. Ros and E. Vergasta.
result Stable CMC hypersurfaces in a ball are either totally geodesic or starshaped.
A higher dimensional generalization of Hersch-Payne-Schiffer inequality for Steklov eigenvaluesmath.DG
In this paper, we generalize the Hersch-Payne-Schiffer inequality for Steklov eigenvalues to higher dimensional case by extending the trick used by Hersch, Payne and Schiffer to higher dimensional manifolds.
We prove an Hersch's type isoperimetric inequality for the third positive eigenvalue on . Our method builds on the theory we developped to construct extremal metrics on Riemannian surfaces in conformal classes for any eigenvalue.
Paper improves estimates for Steklov eigenvalues.
problem Estimating Steklov eigenvalues and their inverses.
method Generalizes previous results using new estimates.
result New estimates for trace and inverse trace of Steklov eigenvalues.
The paper broadens a mathematical correspondence to include more balanced metrics.
problem Extending a mathematical correspondence to a broader class of metrics.
method Using key observations and known theorems to apply results to a new class of metrics.
result The known results can be applied to a larger class of metrics, including those arising from multipolarizations.
Study spectral properties of modified Dirichlet-to-Neumann map on differential forms.
problem Spectral properties of modified Dirichlet-to-Neumann map on differential forms.
method Investigation of self-adjointness and purely discrete spectrum of the operator Λ on coclosed forms.
result Hersch-Payne-Schiffer type inequality relating eigenvalues of Λ to eigenvalues of Hodge Laplacian on the boundary.
We prove that the isoperimetric inequality due to Hersch-Payne-Schiffer for the n-th nonzero Steklov eigenvalue of a bounded simply-connected planar domain is sharp for all n=1,2,... The equality is attained in the limit by a sequence of simply-connected domains degenerating to the disjoint union of n identical disks. …
We try to present an estimate relating the first Dirichlet and Neumann eigenvalues of a compact bordered Riemannian surface.
A theorem of J. Hersch (1970) states that for any smooth metric on , with total area equal to , the first nonzero eigenvalue of the Laplace operator acting on functions is less than or equal to 2 (this being the value for the standard round metric). For metrics invariant under the standard -action on $S^2…
We give explicit isoperimetric upper bounds for all Steklov eigenvalues of a compact orientable surface with boundary, in terms of the genus, the length of the boundary, and the number of boundary components. Our estimates generalize a recent result of Fraser-Schoen, as well as the classical inequalites obtained by Her…
Study shows convergence of anticanonically balanced metrics to Kähler-Einstein metrics on Fano manifolds.
problem Finding anticanonically balanced metrics on Fano manifolds.
method Simplification of Donaldson's proof using Berezin-Toeplitz quantization.
result Sequence of anticanonically balanced metrics converges to Kähler-Einstein metric.
Stability of Lie group homomorphisms and subgroups via Moser type argument.
problem When a deformation of Lie group homomorphisms and subgroups is trivial.
method Moser type argument for compact groups.
result Stability results for compact Lie groups.
Geometric argument proves projection theorems in hyperbolic space.
problem Proving projection theorems for hyperbolic space.
method Geometric argument for orthogonal projections.
result Characterization of purely unrectifiable sets in hyperbolic space.
Study properties of balanced hyperbolic compact complex manifolds.
problem Understanding cohomology and harmonic spaces of balanced hyperbolic manifolds.
method Proved vanishing theorems and Hard Lefschetz-type theorems for balanced hyperbolic compact complex manifolds.
result Non-existence of certain currents on the universal covering space of a balanced hyperbolic manifold.
Minimal harmonic maps proved for specific manifolds.
problem Existence of harmonic maps in fractional Sobolev spaces.
method Developed new tools for fractional Sobolev spaces, including removability and balanced energy estimates.
result Existence of harmonic maps in homotopy classes for certain conditions.
The paper calculates heat kernel and closed geodesic asymptotics for nilpotent coverings.
problem Heat kernel and closed geodesic asymptotics for nilpotent coverings.
method Finite-dimensional rational Floquet-Bloch theory, Pytlik functional, and spectral sums.
result Genuinely local, pointwise higher-order heat-kernel expansions.
Study on existence of balanced metrics on non-Kähler manifolds.
problem Existence of balanced metrics on non-Kähler complex manifolds.
method Analyzes obstructions and constructs examples, focusing on compact quotients of Lie groups.
result Proves non-existence on certain non-Kähler complex parallelizable manifolds and solvmanifolds.
The study examines whether a specific type of hyperbolic manifolds remains unchanged under birational transformations.
problem Birational invariance of balanced hyperbolic manifolds.
method Analysis of the class of balanced hyperbolic manifolds.
result The class of balanced hyperbolic manifolds is birationally invariant.
Study non-Kähler metrics on complex nilmanifolds, proving torus structure under certain conditions.
problem Understanding special non-Kähler metrics on complex nilmanifolds.
method Analyzing locally conformally Kähler, -Gauduchon, balanced, and locally conformally balanced metrics on compact complex manifolds.
result Compact complex nilmanifolds with balanced or -Gauduchon metrics are tori, extending previous results.
New nodal domain theorems for symmetric matrices via signed graphs.
problem Establish nodal domain theorems for symmetric matrices.
method Explore signed graph structure to define nodal domains for any function.
result Improved lower bound estimates for the number of strong nodal domains.
Algorithmic Regularization in Learning Deep Homogeneous Models: Layers are Automatically Balancedcs.LG
Gradient descent balances layer magnitudes in deep neural networks without explicit regularization.
problem Balancing magnitudes across layers in deep neural networks.
method Gradient descent with infinitesimal step size enforces layer magnitude balance.
result Gradient descent automatically balances layer magnitudes without explicit regularization.
Simplified Obata-Vétois argument for Einstein manifolds with nonnegative scalar curvature.
problem Identifying conditions for closed conformally Einstein manifolds to be Einstein.
method Simplified Obata-Vétois argument, identifying a closed interval containing zero.
result Closed conformally Einstein manifolds with nonnegative scalar curvature are Einstein if they satisfy certain conditions.
The study constructs balanced and rigid curves on specific types of hypersurfaces and complete intersections.
problem Constructing balanced and rigid curves on Calabi-Yau and general-type complete intersections.
method Balanced and rigid curves are constructed using specific hypersurfaces and complete intersections.
result Rigid curves of various genera and balanced rational curves of high degrees are constructed.
Study stability of measures on Kähler manifolds with Hamiltonian actions.
problem Stability of measures on Kähler manifolds under group actions.
method Identify and apply momentum mapping criteria for stability, semi-stability, and polystability.
result Various stability criteria for measures on Kähler manifolds.
Paper doubles Hessian estimates for special Lagrangian equation with constraints.
problem Estimating Hessian for special Lagrangian equation under general phase constraints.
method Doubling argument, Alexandrov-type theorems.
result Established Hessian estimates for special Lagrangian equation.
Balanced metrics found on Lie groups and their quotients.
problem Existence of balanced metrics on Lie groups and quotients.
method Proved existence of invariant complex structures and Hermitian balanced metrics on Lie groups and quotients.
result Existence of balanced metrics on Lie groups and quotients, and no pluriclosed metrics.
Study locally conformally balanced metrics on specific Lie algebras.
problem Characterize and classify locally conformally balanced metrics on almost abelian Lie algebras.
method Characterizations and classifications based on specific properties of Lie algebras.
result Classification of six-dimensional almost abelian Lie algebras with locally conformally balanced metrics.
Extends Serrin's symmetry result to model manifolds.
problem Proving symmetry in solutions to a specific PDE on manifolds.
method Uses an extension of Weinberger's argument to prove symmetry.
result Euclidean symmetry result under compatibility assumption.
Proves smoothness and star-shapedness of weak IMCF solutions in hyperbolic space.
problem Analyzing weak inverse mean curvature flow in hyperbolic space.
method Inspired by Alexandrov reflection method, uses Li-Wei result.
result Proves expanding spheres as the only proper weak IMCF on hyperbolic space.
On balanced HKT manifoldsmath.DG
Proves openness of balanced HKT cone and studies hyperholomorphic vector fields.
problem Understanding balanced HKT structures on compact hypercomplex manifolds.
method Analyzes Lie algebra of hyperholomorphic vector fields and proves harmonicity properties.
result Proves openness of balanced HKT cone and non-existence of certain fields.
Double bubbles in and math.DG
We prove the double bubble conjecture in the three-sphere and hyperbolic three-space in the cases where we can apply Hutchings theory: 1) in , each enclosed volume and the complement occupy at least 10% of the volume of ; 2) in , the smaller volume is at least 85% that of the larger. A balanc…
Based on a calibration argument, we prove a Bernstein type theorem for entire minimal graphs over Gauss space by a simple proof.
The paper connects diffeomorphism groups and sphere embeddings, proving a group structure.
problem Understanding the homotopy types of diffeomorphism groups and sphere embeddings.
method Cerf's upgraded proof, scanning maps, canceling handles, Embedding Calculus.
result The monoid of Schoenflies spheres forms a group under connect-sum.
BNRE improves simulation-based inference by producing more conservative posteriors.
problem Overconfident posteriors from current simulation-based inference algorithms risk false inferences.
method Balanced Neural Ratio Estimation (BNRE) that produces more conservative posterior approximations.
result BNRE produces more conservative posterior surrogates on all tested benchmarks and simulation budgets.
Optimizes eigenvalues on surfaces with symmetries.
problem Maximizing Laplace and Steklov eigenvalues on Riemann surfaces with symmetries.
method Simplifies existing techniques for conformal class optimization.
result Proves existence and regularity of maximizers for Laplace and Steklov eigenvalues.
Paper proves depth bounds for taut foliations using instanton Floer homology.
problem Finding depth bounds for taut foliations in sutured manifolds.
method Sutured instanton Floer homology, adapted to monopole and Heegaard Floer settings.
result Dimension of sutured instanton Floer homology bounds minimal depth of taut foliations.
Improves causal inference with observational data by balancing features and weights.
problem Achieving balance in predictive features for causal inference with observational data.
method Integrates balancing weights into representation learning for causal learning.
result Developed an algorithm for accurate estimation of causal effects.
Proves K-stability and superrigidity of certain singular Fano hypersurfaces.
problem Proving K-stability and superrigidity of singular Fano hypersurfaces.
method Inductive argument using information from lower dimensions and adjunction type results for local volumes of singularities.
result Proves birational superrigidity and K-stability of singular Fano hypersurfaces with specific conditions.
Equivalence found between two types of embeddings for Kähler manifolds.
problem Equivalence between two types of embeddings for Kähler manifolds.
method GIT characterization and action of automorphism group on Chow line.
result Equivalence of -balanced and balanced embeddings.
New algorithm balances limited resources for unknown customer types over time.
problem Allocating limited resources to diverse customers with uncertain demands.
method Synthesizes inventory balancing and online learning.
result Performance guarantee is tight, showing both competitive ratio and regret losses are relevant.
The existence of a balanced vertex is proven for geodesic nets with three boundary vertices.
problem Existence of a balanced vertex in geodesic nets with specific boundary conditions.
method Proof of existence on a general two-dimensional Riemannian surface.
result Existence of a balanced vertex for geodesic nets with three unbalanced boundary vertices.
Study solves complex equation on specific types of manifolds.
problem Solving complex Monge-Ampère equation on Kähler manifolds.
method Flow-based arguments to establish existence of smooth solutions.
result Existence of smooth solutions under decreasing right-hand side.
Proves quantitative Alexandrov theorem for capillary surfaces.
problem Proving a quantitative version of the Alexandrov theorem for capillary hypersurfaces.
method Quantitative analysis of Montiel-Ros-type argument.
result Generalizes Julin-Niinikoski's result to capillary case.
Paper provides a formula for translating solitons and singular minimal surfaces.
problem Representing translating solitons and singular minimal surfaces in 3D space.
method Develops a Weierstrass representation formula.
result Solves a general Cauchy problem for the class of surfaces.
This paper argues that the fundamental principle of contemporary financial economics is balanced reciprocity, not the principle of utility maximisation that is important in economics more generally. The argument is developed by analysing the mathematical Fundamental Theory of Asset Pricing with reference to the emergen…
Investigates special metrics in hypercomplex geometry.
problem Characterizing and understanding special hyperhermitian metrics.
method Characterization of hypercomplex structures with Obata holonomy, investigation of quaternionic Gauduchon and balanced metrics, incompatibility results, and introduction of Einstein-type conditions.
result Joyce's manifolds always admit special metrics.