Concave elliptic operators yield concave functions on cohomology.
problem Understanding concave functions on cohomology.
method General construction of concave elliptic operators.
result Generalized Khovanskii-Teissier inequalities.
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48 results for “elliptic generators”
This note shows how independent elliptical distributions minimize the Wasserstein distance.
problem Minimizing the Wasserstein distance between elliptical distributions.
method Analyzing the Wasserstein distance between independent elliptical distributions with the same density generators.
result Independent elliptical distributions minimize their Wasserstein distance from other elliptical distributions with the same density generators.
Researchers compute the cohomology of an elliptic tangent bundle.
problem Computing the cohomology of a specific Lie algebroid.
method Direct computation of cohomology.
result The cohomology of the elliptic tangent bundle is computed.
The paper defines MTCov for skewed elliptical distributions.
problem No specific problem stated, but dealing with skewed elliptical distributions.
method Defined MTCov for generalized skew-elliptical distributions and compared with skewed and non-skewed normal distributions.
result Special formula for MTCov of generalized skew-elliptical distributions.
We give a systematic method to calculate some homological data from the global monodromy of a topological elliptic surface. We apply this method to the cases 1) the transcendental lattice of an extremal elliptic K3 surface, 2) the torsion part of Mordell-Weil group of a general elliptic surface, and 3) the Mordell-Weil…
A guide for solving first-order elliptic boundary value problems.
problem Solving first-order elliptic boundary value problems on manifolds.
method Operator methods and general elliptic boundary conditions.
result Characterization of a new subclass of elliptic boundary conditions.
Rational ellipticity proven for -manifolds with specific quotient properties.
problem Conditions for rational ellipticity in -manifolds.
method Proving rational ellipticity based on quotient properties and manifold submetries.
result Compact, simply connected -manifolds with certain quotient properties are rationally elliptic.
Elliptic Chern characters and Atiyah-Witten formula generalized to double loop spaces.
problem Generalizing classical Atiyah-Witten formula to double loop spaces.
method Constructing elliptic Chern and Bismut-Chern characters, defining elliptic holonomy, and using equivariant twisted parallel transport.
result Established elliptic Atiyah-Witten formula on double loop space.
New proof for curved 3-cohom manifold rational ellipticity.
problem Rational ellipticity of curved manifolds with specific cohomogeneity.
method Proved rationally elliptic for cohomogeneity-three manifolds with positive curvature and no boundary quotient.
result Closed, simply connected, positively curved, cohomogeneity-three manifolds without boundary are rationally elliptic.
Paper proves a Liouville theorem for a generalized elliptic equation on H-type groups.
problem Proving a Liouville theorem for a generalized elliptic equation on H-type groups.
method Proof based on an a priori integral estimate and a generalized differential identity.
result Obtained a Liouville type theorem for the semilinear subcritical elliptic equation on H-type groups.
Elliptical processes generalize Gaussian and Student-t models with fat tails and computational efficiency.
problem Need for models with fat tails and computational tractability.
method Represent elliptical distributions as continuous mixtures of Gaussian distributions, derive closed-form expressions for marginal and conditional distributions.
result Elliptical processes offer advantages in robust regression compared to Gaussian processes.
The paper studies elliptical surfaces in 3D affine space, classifying them based on curvature.
problem Classifying regular elliptical surfaces in affine space based on curvature.
method Defined a moving frame of minimal order for regular elliptical surfaces and derived differential invariants.
result Classified regular elliptical surfaces of constant curvatures up to affine congruence.
Elliptic systems are characterized by Darboux integrability.
problem Characterizing elliptic differential systems with holomorphic solutions.
method Using a complex manifold and associated holomorphic Pfaffian system.
result Elliptic systems are Darboux integrable under generic conditions.
Extends index theorem to uniformly elliptic operators on manifolds.
problem Generalizing index theorem to uniformly elliptic operators.
method Local index theorem on manifolds of bounded geometry.
result Validates multigraded elliptic uniform pseudodifferential operators.
Extends a theorem for first-order elliptic operators on manifolds.
problem Proving the relative index theorem for general first-order elliptic operators.
method Using boundary value problems and graphical decomposition of elliptically regular boundary conditions.
result Proves the relative index theorem for general first-order elliptic operators.
We give a representation theoretical proof of Branson's classification of minimal elliptic sums of generalized gradients. The original proof uses tools of harmonic analysis, which as powerful as they are, seem to be specific for the structure groups SO(n) and Spin(n). The different approach we propose is based on the r…
Method classifies solutions to elliptic problems in disk-like domains.
problem Classifying solutions to overdetermined elliptic problems in topological disks.
method Poincare-Hopf index theorem approach.
result Analogue of Hopf's uniqueness theorem for constant mean curvature spheres in general analytic context.
In this short note we prove that in the case of elliptic curves, the isomorphism of generalized complex structure between -dual manifolds described by Cavalcanti-Gualtieri coincides with the mirror map for elliptic curves described by Polishchuk and Zaslow.
Study the relationship between canonical polynomials and elliptic sequences for elliptic singularities.
problem Understanding the relationship between canonical polynomials and elliptic sequences for elliptic singularities.
method An inductive setup of elliptic germs and comparison of their canonical polynomials.
result The exponents of the canonical polynomial determine the elliptic sequence and vice versa under certain conditions.
Method proves ellipticity of vacuum spacetime boundary problems.
problem Proving ellipticity of boundary value problems for stationary vacuum spacetimes.
method Developed a general method using the projection formalism.
result Proved manifold theorem for moduli space of stationary vacuum spacetimes.
Elliptical processes extend Gaussian models with heavier tails.
problem Regression and classification with non-Gaussian likelihoods or heavy tails.
method Spline normalizing flow for variational inference of elliptical distributions.
result Elliptical processes outperform Gaussian processes in non-Gaussian settings.
Study of 17 surface behaviors and singularities for elliptic Weingarten equations.
problem Characterizing and understanding elliptic Weingarten surfaces and their singularities.
method Phase space analysis and classification of surface behaviors.
result Classification of 17 possible qualitative behaviors for rotational surfaces.
The Basel liquidity formula is extended for elliptical risk-factor changes.
problem Extending the Basel liquidity formula for non-Gaussian risk-factor changes.
method Generalized the formula for multivariate elliptical risk-factor changes, using Fourier approach for expected shortfall calculation.
result The formula tends to be conservative for heavier-tailed distributions.
On orbifold elliptic genusmath.DG
We define orbifold elliptic genus for general orbifolds which generalizes the definition of Borisov and Libgober, and prove their rigidity property.
The study explores finite group actions on elliptic 3-manifolds.
problem Finite, fiber-preserving group actions on elliptic 3-manifolds.
method General construction and restriction to elliptic 3-manifolds, proof for orientation-reversing and fiber-preserving diffeomorphisms, analysis of each type of elliptic 3-manifold.
result A presentation for the quotient space under finite group actions is constructed.
Unified derivation of stochastic order conditions for elliptical distributions.
problem Classifying multivariate elliptical distributions based on stochastic orders.
method Established an identity for comparing expectations of functions of elliptical vectors and used it to derive conditions for stochastic orders.
result Unified derivation of conditions for various stochastic orders in multivariate elliptical distributions.
No projective structure found on foliations of elliptic curves.
problem Existence of transversely projective structures on foliations.
method Analyzing foliations on the product of two elliptic curves.
result Generic nonsingular turbulent foliations do not have transversely projective structures.
The paper defines new modular forms from almost complex manifolds and derives anomaly cancellation formulas.
problem Anomaly cancellation in almost complex manifolds.
method Defined a generalized elliptic genus and derived SL(2,Z) modular forms.
result Derived anomaly cancellation formulas and divisibility results for holomorphic Euler characteristic.
We prove several vanishing theorems for a class of generalized elliptic genera on foliated manifolds, by using classical equivariant index theory. The main techniques are the use of the Jacobi theta-functions and the construction of a new class of elliptic operators associated to foliations.
Study boundary value problems for elliptic operators on manifolds.
problem Characterize and analyze boundary conditions for first-order elliptic differential operators.
method Develops a new framework for elliptic boundary conditions, proving equivalence and regularity of solutions.
result Elliptic boundary conditions yield a Fredholm operator on compact manifolds.
The paper extends elliptic genus and proves anomaly cancellation formulas for almost complex manifolds.
problem Anomaly cancellation formulas for almost complex manifolds.
method Extended elliptic genus, proved weak Jacobi forms, derived SL_2(Z) modular forms.
result New anomaly cancellation formulas of characteristic forms for almost complex manifolds.
The paper calculates moments and conditional risks for skewed elliptical distributions.
problem Estimating moments and tail conditional risks for skewed elliptical distributions.
method Derives explicit expressions for multivariate doubly truncated moments and conditional risks for generalized skew-elliptical distributions.
result Explicit formulas for multivariate doubly truncated moments and conditional risks are derived for various skewed elliptical distributions.
Characterizes stably elliptic elements in Lie groups and their properties.
problem Understanding stably elliptic elements in Lie groups and their geometric and algebraic properties.
method Characterization through fixed point algebra and Weyl group action; relates to maximal invariant cones and compactness of order intervals.
result Connected components of stably elliptic elements can be described using Weyl group action on a compactly embedded Cartan subalgebra.
Study the heat operator of a transversally elliptic operator on Lie groups.
problem Spectral properties and convergence of a heat operator on Lie groups.
method Review spectral properties, define character, estimate heat operator convergence.
result Estimate of determines convergence of the character.
We establish a general theorem improving regularity of solutions of elliptic pseudodifferential equations. It allows to resolve in a unified way the regularity issue for a broad class of nonlinear elliptic equations and systems appearing in different areas of geometry and analysis.
Surveying the signature theorem, researchers cancel anomalies on elliptic surfaces.
problem Anomaly cancellation in elliptic surface physics.
method Application of the Riemann-Roch-Grothendieck-Quillen formula to elliptic curves.
result Local and global anomalies can be canceled on Jacobian elliptic surfaces.
Every element of PU(2,1) can be decomposed into at most 4 special elliptic isometries.
problem Understanding the length of elements in PU(2,1) relative to special elliptic isometries.
method Generalizing the involution length of the complex hyperbolic plane, calculating the -length of PU(2,1) and describing decompositions of isometries.
result Every element of PU(2,1) can be decomposed into at most 4 special elliptic isometries.
Paper studies rigidity phenomena for elliptic systems on Riemannian manifolds.
problem Local radial rigidity of elliptic systems on Riemannian manifolds.
method Reduction to singular ordinary differential equations of Euler type.
result Local uniqueness and existence results for solutions with prescribed initial jets.
Extends T-duality to non-principal torus actions with elliptic tangent bundles.
problem Classifying and understanding non-principal torus actions with singularities.
method Introduces elliptic tangent bundle to control singularities, uses it to define connections and transport generalized complex structures via T-duality.
result New insights into the classification of torus actions and transport of generalized complex structures.
Flow proves Kähler-Einstein on minimal elliptic surfaces.
problem Proving Kähler-Einstein on minimal elliptic surfaces.
method Conical Kähler-Ricci flow with semi-ampleness assumption.
result Flow converges to Kähler-Einstein on canonical model.
Proves C^2,alpha estimates for elliptic equations on hyperkähler manifolds.
problem Elliptic equations on hypercomplex manifolds.
method Proves C^2,alpha estimates under suitable assumptions.
result Solutions to specific elliptic equations on hyperkähler manifolds satisfy C^2,alpha estimates.
First time projective elliptic genera constructed for oriented manifolds.
problem Defining and proving properties of projective elliptic genera.
method Topological construction and analytic interpretation via fractional index theorem.
result Modularity properties of projective elliptic genera proven.
We study boundary value problems for linear elliptic differential operators of order one. The underlying manifold may be noncompact, but the boundary is assumed to be compact. We require a symmetry property of the principal symbol of the operator along the boundary. This is satisfied by Dirac type operators, for instan…
A functional ansatz is developed which gives certain elliptic solutions of the Witten-Dijkgraaf-Verlinde-Verlinde (or WDVV) equation. This is based on the elliptic trilogarithm function introduced by Beilinson and Levin. For this to be a solution results in a number of purely algebraic conditions on the set of vectors …
Continuity method yields Kähler-Einstein metric on elliptic surfaces.
problem Proving convergence of continuity method on elliptic Kähler surfaces.
method Continuity method applied to Kähler metrics on elliptic surfaces.
result Continuity method converges to Kähler-Einstein metric.
An elliptic theory is constructed for operators acting in subspaces defined via odd pseudodifferential projections. Subspaces of this type arise as Calderon subspaces for first order elliptic differential operators on manifolds with boundary, or as spectral subspaces for self-adjoint elliptic differential operators of …
The singular sets of degenerate and nonlocal elliptic equations on Poincaré-Einstein manifoldsmath.DG
The paper studies degenerate and nonlocal elliptic operators on Poincaré-Einstein manifolds.
problem Understanding the singular sets of degenerate and nonlocal elliptic operators on Poincaré-Einstein manifolds.
method Developing quantitative differentiation theory, stratification, Minkowski estimates, and ε-regularity results.
result Uniform Hausdorff measure estimates for the singular sets of degenerate/singular elliptic operators.
Study calculates tail risk for various mixture distributions.
problem Estimating tail risk for complex distribution mixtures.
method Analyzes tail conditional expectation for location-scale mixtures of elliptical distributions.
result Developed methods for calculating tail risk in various distributions.