Related papers: Some Uniforme Estimates for Scalar Curvature Type …
Smooth hypoellipticity for scalar equations is quite well understood presently. On the other hand, much remains to be done for systems and/or at different levels of regularity and in particular for $L^1$-hypoellipticity. In this article we…
A complete classification of isotropic vector equations of the geometric type that possess higher symmetries is proposed. New examples of integrable multi-component systems of the geometric type and their auto-Backlund transformations are…
We derive extrinsic curvature estimates for compact disks embedded in $\mathbb{R}^3$ with nonzero constant mean curvature.
We give some uniform estimates for constant mean curvature solutions of the conformal vacuum Einstein constraint equations on compact manifolds. Existence of those solutions was given in a paper by J. Isenberg.
We prove a constant rank theorem for the second fundamental form of the spatial convex level surfaces of solutions to equations $u_t=F(\n^2u, \n u, u, t)$ under a structural condition, and give a geometric lower bound of the principal…
In this paper we consider Yamabe type problem for higher order curvatures on manifolds with totally geodesic boundaries. We prove local gradient and second derivative estimates for solutions to the fully nonlinear elliptic equations…
In the note, the Euler scaling is used to study a certain scenario of potential Type II blowups of solutions to the Navier-Stokes equations.
We show there are precisely 15 inhomogeneous biquotients of the form $Sp(3)// Sp(1)^2$ and show that at least 8 of them admit metrics of quasi-positive curvature.
This note provides new closed forms evaluations of a few classes of exponential sums associated with elliptic curves and hyperelliptic curves.
Special cases of Weber-Schafheitlin type integrals are evaluated analytically.
In this study, a new form of quadratic spline is obtained, where the coefficients are determined explicitly by variational methods. Convergence is studied and parity conservation is demonstrated. Finally, the method is applied to solve…
The main result of this paper gives a plenary proof on the curvature estimates for $k$ curvature equations with general right hand sides with $n<2k$ based on a concavity inequality. We further give a explicit lower bound of the inequality.
Analysis of the generalized Weierstrass-Enneper system includes the estimation of the degree of indeterminancy of the general analytic solution and the discussion of the boundary value problem. Several different procedures for constructing…
In this article we present new gradient estimates for positive solutions to a class of nonlinear elliptic equations involving the f-Laplacian on a smooth metric measure space. The gradient estimates of interest are of Souplet-Zhang and…
In this article, we study the invariant differential forms which a correspondence of curves admits. We also try to classify the correspondences of $\mathbb{P}^1$ that admits such invariant differential forms.
We show that results about spaces or moduli spaces of positive scalar curvature metrics proved using index theory can typically be extended to non-negative scalar curvature metrics. We illustrate this by providing explicit generalizations…
In this paper, we establish a curvature estimate for semi-convex solutions of Hessian equations in hyperbolic space. We also obtain a curvature estimate for admissible solutions to prescribed curvature measure type problem in hyperbolic…
By the multiple-scale method some new approximate absorbing boundary conditions for the Schr\"odinger type equations are obtained.
We derive level set version of partial uniform ellipticity for symmetric concave functions. This suggests an effective approach to investigate second order fully nonlinear equations of elliptic and parabolic type.
This paper concerns local gradient estimates to solutions of general conformally invariant fully nonlinear elliptic equations of second order.