Research interests
Jae-Seong Cho
The area of my research centers around both algebraic and analytic questions of several complex
variables.
In
order to study a number of important questions on smoothly bounded domains,
it is often useful
to investigate boundary behavior of a solution of the inhomogeneous Cauchy-Riemann equation.
For
example, the questions of
- smooth extendability of holomorphic functions from the boundary,
- regularity at the boundary of biholomorphic maps
- boundary behavior of the Bergman metric
are all depending on having good
estimates near the boundary for the solution to $\bar{\partial}$-equation.
I am currently working with David W. Catlin on the question of
- finding a sharp estimate on smoothly bounded pseudoconvex domains.
The question of obtaining sharp subelliptic estimates has been inspiring me to investigate
both algebraic and analytic invariants inherited from complex analytic varieties and real smooth
hypersurfaces.
Click Research Interests for more details.
- A Monotone Property of Subelliptic Estimates under Ideal Inclusion. (in preparation)
- Types and Sharp Subelliptic Estimates on Regular Coordinate Domains, with David W. Catlin. (in
preparation)
- Sharp Subelliptic Estimates on Rigid Homogeneous Domains in C^3. (in progress)
- (With D. W. Catlin)
Sharp Estimates for the d-bar Neumann Problem on Regular Coordinate Domains. (submitted)
-
Monotonicity of Subelliptic Estimates on Rigid Peudoconvex Domains. (submitted)
- An Algebraic Generalization of Subelliptic Multipliers, Thesis (2006).
-
An Algebraic Version of Subelliptic Multipliers, Mich. Math. J. Vol. 54 (2006).
- Complete prolongation and the Frobenius integrability for overdetermined systems ofpartial differential equations,
J. Korean Math. Soc. 39 (2002), no. 2, 237 -252 (with Han, C.K.)