Hessian estimates to special Lagrangian equation on general phases with constraints

2021 ◽  
Vol 61 (1) ◽  
Author(s):  
Xingchen Zhou
Keyword(s):  
Lagrangian Equation ◽  
Special Lagrangian ◽  
Hessian Estimates ◽  
Special Lagrangian Equation

scholarly journals The Degenerate Special Lagrangian Equation on Riemannian Manifolds

2018 ◽  
Vol 2020 (9) ◽  
pp. 2832-2863
Author(s):  
Matthew Dellatorre
Keyword(s):  
Riemannian Manifold ◽  
Dirichlet Problem ◽  
Riemannian Manifolds ◽  
Duality Theory ◽  
Continuous Solutions ◽  
Lagrangian Equation ◽  
Base Manifold ◽  
Special Lagrangian ◽  
Euclidean Setting ◽  
Special Lagrangian Equation

Abstract We show that the degenerate special Lagrangian equation (DSL), recently introduced by Rubinstein–Solomon, induces a global equation on every Riemannian manifold, and that for certain associated geometries this equation governs, as it does in the Euclidean setting, geodesics in the space of positive Lagrangians. For example, geodesics in the space of positive Lagrangian sections of a smooth Calabi–Yau torus fibration are governed by the Riemannian DSL on the base manifold. We then develop their analytic techniques, specifically modifications of the Dirichlet duality theory of Harvey–Lawson, in the Riemannian setting to obtain continuous solutions to the Dirichlet problem for the Riemannian DSL and hence continuous geodesics in the space of positive Lagrangians.

scholarly journals The degenerate special Lagrangian equation

2017 ◽  
Vol 310 ◽  
pp. 889-939 ◽  
Author(s):  
Yanir A. Rubinstein ◽  
Jake P. Solomon
Keyword(s):  
Lagrangian Equation ◽  
Special Lagrangian ◽  
Special Lagrangian Equation

scholarly journals Singular BPS boundary conditions in $$ \mathcal{N} $$ = (2, 2) supersymmetric gauge theories

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Tadashi Okazaki ◽  
Douglas J. Smith
Keyword(s):  
String Theory ◽  
Boundary Conditions ◽  
Gauge Theories ◽  
Holomorphic Curve ◽  
Two Dimensional ◽  
Supersymmetric Gauge Theories ◽  
Special Lagrangian ◽  
Supersymmetric Gauge ◽  
M Theory

Abstract We derive general BPS boundary conditions in two-dimensional $$ \mathcal{N} $$ N = (2, 2) supersymmetric gauge theories. We analyze the solutions of these boundary conditions, and in particular those that allow the bulk fields to have poles at the boundary. We also present the brane configurations for the half- and quarter-BPS boundary conditions of the $$ \mathcal{N} $$ N = (2, 2) supersymmetric gauge theories in terms of branes in Type IIA string theory. We find that both A-type and B-type brane configurations are lifted to M-theory as a system of M2-branes ending on an M5-brane wrapped on a product of a holomorphic curve in ℂ2 with a special Lagrangian 3-cycle in ℂ3.

scholarly journals Special Lagrangian cones with higher genus links

2006 ◽  
Vol 167 (2) ◽  
pp. 223-294 ◽  
Author(s):  
Mark Haskins ◽  
Nikolaos Kapouleas
Keyword(s):  
Special Lagrangian ◽  
Higher Genus
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