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.
We exhibit infinitely many, explicit special Lagrangian isolated singularities that admit no asymptotically conical special Lagrangian smoothings. The existence/ nonexistence of such smoothings is an important component of the current efforts to understand which singular special Lagrangians arise as limits of smooth sp…
Study on deformations of special Lagrangians with boundary in Calabi-Yau manifolds.
We study gluings of asymptotically cylindrical special Lagrangian submanifolds in asymptotically cylindrical Calabi--Yau manifolds. We prove both that there is a well-defined gluing map, and, after reviewing the deformation theory for special Lagrangians, prove that this gluing map defines a local diffeomorphism from m…
We introduce special Lagrangian submanifolds in C^m and in (almost) Calabi-Yau manifolds, and survey recent results on singularities of special Lagrangian submanifolds, and their application to the SYZ Conjecture. The paper is aimed at graduate students in Geometry, String Theorists, and others wishing to learn the sub…
We study special Lagrangian cones in $\C^n$ with isolated singularities. Our main result constructs an infinite family of special Lagrangian cones in $\C^3$ each of which has a toroidal link. We obtain a detailed geometric description of these tori. We prove a regularity result for special Lagrangian cones in $\C^3$ wi…
Quantifies closeness of special Lagrangians under Floer conditions.
Construct special Lagrangian pair of pants in n dimensions.
In this paper, which is a natural continuation of our previous paper math.DG/0504557, we describe some special Lagrangians of cohomogeneity one in the resolved conifold. Our main result gives a foliation of the resolved conifold by T^2-invariant special Lagrangians, where the generic leaf is topologically T^2 X R. We a…
Study special Lagrangian moduli spaces with boundary.
The paper proves constant rank theorems for special Lagrangian equations.
Constructs special Lagrangian 3-spheres in non-Kähler compact threefolds.
Tropical curves match to special Lagrangian shapes.
The purpose of this paper is to give an application of the gluing theorem for special Lagrangian submanifolds of a Calabi-Yau 3-fold. We proved a gluing theorem before to smooth a codimension-two singularity of a particular special Lagrangian submanifold. In this paper we will show that this theorem can be applied to m…
This is the first in a series of papers on special Lagrangian submanifolds in C^m. We study special Lagrangian submanifolds in C^m with large symmetry groups, and give a number of explicit constructions. Our main results concern special Lagrangian cones in C^m invariant under a subgroup G in SU(m) isomorphic to U(1)^{m…
New Lagrangian and special Lagrangian examples found in complex space.
The paper proves transversality for special Lagrangian submanifolds in a 6D manifold.
In this paper we describe the cohomogeneity one special Lagrangian 3-folds in the cotangent bundle of the 3-sphere, also known in the physics literature as a deformed conifold. Our main result gives a global foliation of the deformed conifold by T^2-invariant special Lagrangian 3-folds, where the generic leaf is topolo…
Special Lagrangian submanifolds emerge from K3 surface collapse.
New homogeneous special Lagrangian submanifolds discovered in nearly Kähler CP3.
The abstract discusses special Lagrangians and their flow, proving conjectures and observing related phenomena.
Butscher, D. Lee, Y. Lee, and Joyce constructed a special Lagrangian submanifold by gluing a Lawlor neck into a transverse intersection point of two special Lagrangian submanifolds. We prove a uniqueness theorem for the gluing of flat special Lagrangian tori of real dimension 3 in a flat complex torus of complex dimens…
This paper studies special Lagrangian submanifolds and their deformations.
Estimates for special Lagrangian curvature equations in critical and convex cases.
Paper proves uniqueness of special Lagrangian pair in Calabi-Yau 3-fold.
Proves conditions for nearby special Lagrangians in Calabi-Yau manifolds.
We introduce a notion of vanishing Maslov index for lagrangian varifolds and lagrangian integral cycles in a Calabi-Yau manifold. We construct mass-decreasing flows of lagrangian varifolds and lagrangian cycles which satisfy this condition. The flow of cycles converges, at infinite time, to a sum of special lagrangian …
Geodesics in positive Lagrangian spaces map to special Lagrangian cylinders.
This paper gives a leisurely introduction to Calabi-Yau manifolds and special Lagrangian submanifolds from the differential geometric point of view, followed by a survey of recent results on singularities of special Lagrangian submanifolds, and their application to the SYZ Conjecture. It is aimed at graduate students i…
This is the second in a series of papers constructing explicit examples of special Lagrangian submanifolds in C^m. The first paper was math.DG/0008021, which studied special Lagrangian m-folds with large symmetry groups. The third is math.DG/0010036, which uses ideas from this paper to construct families of special Lag…
Generalizes Thomas-Yau theorem for special and minimal Lagrangians.
We give a necessary and sufficient condition for a special Lagrangian submanifold in C^n constructed by Lawlor being also special Lagrangian in C^n with the Fubini-Study form.
We derive formulas for the mean curvature of special Lagrangian 3-folds in the general case where the ambient 6-manifold has intrinsic torsion. Consequently, we are able to characterize those SU(3)-structures for which every special Lagrangian 3-fold is a minimal submanifold. In the process, we obtain an obstruction to…
Proves smoothness and estimates for special Lagrangian solutions with semi-convexity.
Researchers prove uniqueness of certain cylindrical tangent cones for special Lagrangians.
We show the existence of special Lagrangian tori on one family of Borcea-Voisin threefolds. We also construct a family of special Lagrangian submanifolds on the total space of the canonical line bundle of projective spaces.
This paper extends to dimension 4 the results in the article "Second Order Families of Special Lagrangian 3-folds" by Robert Bryant. We consider the problem of classifying the special Lagrangian 4-folds in C^4 whose fundamental cubic at each point has a nontrivial stabilizer in SO(4). Points on special Lagrangian 4-fol…
Constructs special Lagrangian submanifolds in Calabi-Yau 3-folds.
Study on singularities in Lagrangian mean curvature flow with special Lagrangian cones.
In this paper, the relationship between the existence of special lagrangian submanifolds and the collapsing of Calabi-Yau manifolds is studied. First, special lagrangian fibrations are constructed on some regions of bounded curvature and sufficiently collapsed in Ricci-flat Calabi-Yau manifolds. Then, in the opposite d…
I point out some very elementary examples of special Lagrangian tori in certain Calabi-Yau manifolds that occur as hypersurfaces in complex projective space. All of these are constructed as real slices of smooth hypersurfaces defined over the reals. This method of constructing special Lagrangian submanifolds is well kn…
We construct smooth families of compact special Lagrangian submanifolds embedded in some toric hyper-K\"ahler manifolds, which never become holomorphic Lagrangian submanifolds via any hyper-Kähler rotations. These families converge to special Lagrangian immersions with self-intersection points in the sense of current…
We make a conjecture about mean curvature flow of Lagrangian submanifolds of Calabi-Yau manifolds, expanding on \cite{Th}. We give new results about the stability condition, and propose a Jordan-Hölder-type decomposition of (special) Lagrangians. The main results are the uniqueness of special Lagrangians in hamiltonian…
Study Neumann problem for special Lagrangian type equations.
Paper doubles Hessian estimates for special Lagrangian equation with constraints.
Proves Hessian estimates for special Lagrangian equation with new proofs.
The paper constructs solutions with infinite-time singularities in Lagrangian mean curvature flow.
Constructs finite-time singularities in Lagrangian mean curvature flow with precise dynamics.
Having fixed a Kaehler class and the unique corresponding hyperkaehler metric, we prove that all special Lagrangian submanifolds of an irreducible symplectic 4-fold X are bi-Lagrangian and that they are obtained by complex submanifolds via a sort of "hyperkaehler rotation trick"; thus they retain part of the rigidity o…