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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.

168,657 papers · 148 categories

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0111 · Oct 202019922001200920172026
8 results for “rigidity-flexibility”
Hyperbolic Monge-Ampère Equation on a Cylinder: Well-Posedness and Stabilitymath.AP

Paper develops a framework for hyperbolic Monge-Ampère equation on strips, proving well-posedness and stability.

problem Addressing the rigidity-flexibility dichotomy for wrinkled patterns in thin elastic sheets.
method Develops hodograph transformation and parametrix-corrector decomposition to handle corner singularities and prove well-posedness.
result Proves existence and uniqueness of hodograph weak solutions and derives energy estimates for stability.
hyperbolic Monge-Ampère equationrigidity-flexibilitythin elastic sheetshodograph transformationcorner singularities
2025-09-29abs ↗pdf ↗
Choosing points on cubic plane curves: rigidity and flexibilitymath.AG

Study on choosing points on cubic curves, answering some questions about their flexibility.

problem Determining if algebraic structures can continuously choose points on cubic plane curves.
method Analyzing the flex points and sextatic points of cubic plane curves.
result Affirmative answer for n=9n=9 and 18, negative for infinitely many nn.
cubic plane curvesflex pointssextatic pointsrigidityflexibility
2021-01-11abs ↗pdf ↗
Rigidity and Flexibility of Isometric Extensionsmath.AP

The paper explores rigidity and flexibility of isometric extensions with critical Hölder exponent.

problem The critical Hölder exponent in isometric extensions and its implications.
method Convex integration and construction of isometric extensions.
result The Hölder exponent $θ_0= rac12$ is critical, with extensions violating the tangential connection for $θ< rac12$.
isometric extensionsrigidityflexibilityHölder exponentconvex integration
2020-10-01abs ↗pdf ↗
Review of the Exponential and Cayley Map on SE(3) as relevant for Lie Group Integration of the Generalized Poisson Equation and Flexible Multibody Systemsmath.DG

This paper summarizes closed-form relations for SE(3) maps and their derivatives.

problem Closed-form expressions for SE(3) maps and their derivatives are scattered in the literature.
method Summarizes and provides proofs for relevant closed-form relations of the exponential and Cayley map on SE(3).
result Provides an implicit generalized-alpha scheme for rigid/flexible multibody systems using the Cayley map.
SE(3)Exponential mapCayley mapLie group integrationGeneralized-alpha scheme
2023-03-14abs ↗pdf ↗
Conserved quantities in General Relativity: the case of initial data sets with a noncompact boundarymath.DG

The study extends conserved quantities theory to non-compact boundary initial data sets.

problem Extending conserved quantities theory to initial data sets with non-compact boundaries.
method Analysis of scalar curvature and mean curvature in the interior and boundary.
result Rigidity/flexibility phenomena in positive mass theorems and Penrose inequalities.
General RelativityConserved QuantitiesInitial Data SetsNon-Compact BoundaryScalar Curvature
2021-03-10abs ↗pdf ↗
Rigidity and flexibility under spectral Ricci lower bounds and mean-convex boundarymath.DG

Sharp spectral extension of rigidity theorem for mean-convex manifolds.

problem Rigidity and flexibility of manifolds with mean-convex boundary and nonnegative Ricci curvature.
method Spectral Ricci lower bounds and mean-convex boundary conditions.
result Sharp spectral extension of rigidity theorem for specific conditions.
Riemannian manifoldsrigidityflexibilityspectral Riccimean-convex boundary
2026-05-12abs ↗pdf ↗