2 citations · 5 across the 10 of their papers we have counts for
11 papers
The second variation of 2-spheres in the 2n-sphere
Gavin Ball, Jesse Madnick
We prove sharp upper and lower bounds for the Morse index and nullity of linearly full branched minimal 2-spheres in the round 2n-sphere. In particular, we show that the Morse inde…
Gauge theory on : explicit Sp(2)-instantons, HYM connections, and Spin(7)-instantons
Izar Alonso, Jesse Madnick, Emily Autumn Windes
We construct and classify -invariant -instantons with gauge groups and over the Calabi manifold , the unique non-flat, complete, ir…
On Sp(n)-Instantons and the Fourier-Mukai Transform of Complex Lagrangians
Jesse Madnick, Emily Autumn Windes
The real Fourier-Mukai (RFM) transform relates calibrated graphs to so-called "deformed instantons" on Hermitian line bundles. We show that under the RFM transform, complex Lagrang…
The Morse index of quartic minimal hypersurfaces
Gavin Ball, Jesse Madnick, Uwe Semmelmann
The homogeneous minimal hypersurfaces in have , or distinct (constant) principal curvatures. While the Morse index and nullity have been calculated for all s…
Calibrated Geometry in Hyperkahler Cones, 3-Sasakian Manifolds, and Twistor Spaces
Benjamin Aslan, Spiro Karigiannis, Jesse Madnick
We systematically study calibrated geometry in hyperkähler cones , their 3-Sasakian links , and the corresponding twistor spaces , emphasizing the rel…
A Spinorial Hopf Differential for Associative Submanifolds
Gavin Ball, Jesse Madnick
Given a CMC surface in , its traceless second fundamental form can be viewed as a holomorphic section called the Hopf differential. By analogy, we show that for an associative…
Associative Submanifolds of Squashed 3-Sasakian Manifolds
Gavin Ball, Jesse Madnick
Every compact 3-Sasakian 7-manifold admits a canonical 2-parameter family of co-closed -structures for , as well as a foliation by -asso…
The Second Variation for Null-Torsion Holomorphic Curves in the 6-Sphere
Jesse Madnick
In the round 6-sphere, null-torsion holomorphic curves are fundamental examples of minimal surfaces. This class of minimal surfaces is quite rich: By a theorem of Bryant, extended…
Associative Submanifolds of the Berger Space
Gavin Ball, Jesse Madnick
We study associative submanifolds of the Berger space SO(5)/SO(3) endowed with its homogeneous nearly-parallel G2-structure. We focus on two geometrically interesting classes: the…
The Mean Curvature of First-Order Submanifolds in Exceptional Geometries with Torsion
Gavin Ball, Jesse Madnick
We derive formulas for the mean curvature of associative 3-folds, coassociative 4-folds, and Cayley 4-folds in the general case where the ambient space has intrinsic torsion. Conse…
The Mean Curvature of Special Lagrangian 3-folds in SU(3)-Structures with Torsion
Gavin Ball, Jesse Madnick
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 charact…