Homepage of Sagun Chanillo

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Publications List

Recent Publications

• Conformal Geometry and the Composite Membrane Problem
• Embedded Three-Dimensional CR Manifolds and the Non-Negativity of Paneitz Operators
  (with H.-L. Chiu and Paul Yang, to appear Contemp. Math. of the AMS)
• A Remark on the Geometry of Uniformly Rotating Stars(with Georg Weiss)
• Wave Equations associated to Liouville Systems and Constant Mean Curvature Equations( with Po-lam Yung)
• An Improved Strichartz Estimate for Systems with Divergence Free data ( with Po-Lam Yung)
• Embeddability for Three Dimensional Cauchy-Riemann Manifolds and CR Yamabe Invariants
  (with Hung-Lin Chiu and Paul Yang)
• Isoperimetric Inequalities and Volume Comparison theorems on CR manifolds(with Paul Yang)
• Regularity of the Minimizers in the Composite Membrane Problem in R^2(with Carlos Kenig and Tung To)
• Subelliptic Bourgain-Brezis estimates on Groups (with Jean Van Schaftingen)
• Sharp Global Bounds for the Hessian on Pseudo-Hermitian Manifolds( with J.J. Manfredi)
• Weak Uniqueness and Partial Regularity for the Composite Membrane Problem(with C. Kenig)
• Schrodinger Equations on Complex Semi-simple Lie Groups
• Plateau Problem-H Surface Eqn.(A. Malchiodi)

Some Older Publications

• Non-Linear Eigenvalues and Analytic Hypoellipticity (B. Helffer, A. Laptev)
• Composite Membranes and Symmetry Breaking (D. Grieser, K. Kurata, M. Imai, I. Ohnishi)
• The Free Boundary Problem for Composite Membranes, Contemporary Math. of the AMS v. 268, (2000)(D. Grieser, K. Kurata)
• The Conformal Plate Buckling Eqn.(M. Kiessling)
• The Difference of Topology in Changing Sign Yamabe Problems, the case of two masses on S^3 (A. Bahri)
• Surfaces with Prescribed Gauss Curvature( A statistical Mechanics approach)( with M. Kiessling)
• Level lines of solutions to Non-Linear PDE in two dimensions (X. Cabre)
• First eigenvalue of the Hodge Laplacian (F. Treves)
• Local Exactness in Differential Complexes (Francois Treves)
• Borg-Levinson Theorem and Inverse Problems for the Dirichlet to Neumann Map.
• Liouville's Eqn. and Conformally Invariant Systems of PDE of Liouville type, Toda Lattices (M. Kiessling)
• Continuity of solutions to Divergence form Elliptic eqns. in R^2 and Compensated Compactness (Yanyan Li)
• On Diameters of Uniformly Rotating white dwarf stars( with Yanyan Li)
• Symmetry and Symmetry Breaking of Solutions to Non-Linear PDE in Physics and Geometry(M. Kiessling)
• Nodal geometry on Riemannian Manifolds(with B. Muckenhoupt)

Research Monograph on Jacobi Polynomials

Optimal Weak type Inequalities for the Partial Cesaro Sum operator for Jacobi Polynomials

Course Information( Spring 2013, Math 432, Introduction to Differential Geometry, TW5, 3.20-4.40, ARC 206)

Grading policy for the course.

List of homework problems.

Supplementary problems from Do Carmo.

Supplementary problems on Metric and first fundamental form from Do Carmo.

Supplementary exercises on the Gauss map.

Homework, Quiz and Exam Announcements

Final Homework submission: pg 227, 1,15; pg 237, 3, 6, pg 260, 1.

FINAL EXAM is on FRIDAY MAY 10th 12-3pm

Mid-term exam 2: 0-35 F, 36-50D, 51-62 C, 63-72 C+, 73-82B, 83-87B+, 88-100 A. Average: 64, Highest score : 100.

Mid-term 1: 0-42F, 43-52D, 53-66C, 67-72 C+, 73-79 B, 80-85 B+, 86- A

Average: 70, Highest score: 93, Lowest score 36.

Here are the solutions to Test 1.

A detailed list of topics on test 1 can be found here.

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Some Interesting Articles related to Mathematics

A short history of Mathematics in 20th century India Artless Innocents and Ivory Tower Sophisticates

CR Geometry and the work of Pancharatnam.

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Maintained by chanillo[at]math[dot]rutgers[dot]edu and last modified 3/1/2013