Related papers: Morse-Darboux lemma for surfaces with boundary
We show how the rotation and translation fields of a surface, introduced by G. Darboux, may be used to obtain short proofs of a well-known theorem (that reads that the total mean curvature of a surface is stationary under an infinitesimal…
We prove a global uniform Artin-Rees lemma type theorem for sections of ample line bundles over smooth projective varieties. This result is used to prove an Artin-Rees lemma for the polynomial ring with uniform degree bounds. The proof is…
We prove partial and full boundary regularity for manifold constrained $p(x)$-harmonic maps.
It is proved that a generic simple, closed, piecewise regular curve in space can be the boundary of only finitely many developable surfaces with nonvanishing mean curvature. The relevance of this result in the context of the dynamics of…
An exact analytic solution is obtained for a uniformly expanding, neutral, infinitely conducting plasma sphere in an external dipole magnetic field. The electrodynamical aspects related to the radiation and transformation of energy were…
We establish rigidity results for ancient solutions to the free boundary mean curvature flow in manifolds with convex boundary. In particular, we show that any free boundary minimal hypersurface of Morse index I admits an I-parameter family…
We solve the problem on flat extensions of a generic surface with boundary in Euclidean 3-space, relating it to the singularity theory of the envelope generated by the boundary. We give related results on Legendre surfaces with boundaries…
We study the Morse index of minimal surfaces with free boundary in a half-space. We improve previous estimates relating the Neumann index to the Dirichlet index and use this to answer a question of Ambrozio, Buzano, Carlotto, and Sharp…
In this paper, we prove a general Schwarz lemma at the boundary for holomorphic mappings from the polydisc to the unit ball in any dimensions. For the special case of one complex variable, the obtained results give the classic boundary…
We consider an inverse problem arising in corrosion detection. We prove a stability result of logarithmic type for the determination of the corroded portion of the boundary and impedance by two measurements on the accessible portion of the…
We present sufficient conditions for the existence of a periodic solution for a class of systems describing the periodically forced motion of a massive point on a compact surface with a boundary.
In this paper, the spinor formulation of Darboux frame on an oriented surface is given. Also, the relation between the spinor formulation of Frenet frame and Darboux frame are obtained.
We consider the Zariski-Lipman Conjecture on free module of derivations for algebraic surfaces. Using the theory of non-complete algebraic surfaces, and some basic results about ruled surfaces, we will prove the conjecture for several…
We consider smooth solutions to the Monge-Amp`ere equation subject to mixed boundary conditions on annular domains. We establish global $C^2$ estimates when the boundary of the domain consists of two smooth strictly convex closed…
We investigate manifolds with boundary in noncommutative geometry. Spectral triples associated to a symmetric differential operator and a local boundary condition are constructed. For a classical Dirac operator with a chiral boundary…
We study the algebraic boundary of a convex semi-algebraic set via duality in convex and algebraic geometry. We generalize the correspondence of facets of a polytope to the vertices of the dual polytope to general semi-algebraic convex…
We provide an elementary derivation of an orthogonal coordinate system for boundary layers around evolving smooth surfaces and curves based on the signed-distance function. We go beyond previous works on the signed-distance function and…
We prove an extension of the well-known combinatorial-topological lemma of E. Sperner to the case of infinite-dimensional cubes. It is obtained as a corollary to an infinitary extension of the Lebesgue Covering Dimension Theorem.
We prove nonlinear lower bounds and commutator estimates for the Dirichlet fractional Laplacian in bounded domains. The applications include bounds for linear drift-diffusion equations with nonlocal dissipation and global existence of weak…
The purpose of this note is to give an (esentially optimal) effective version of Matsusaka's Big theorem for smooth projective surfaces.