相关论文: Strong holomorphic Morse inequalities on non-compa…
The authors give a complete classification of projective threefolds admitting a holomorphic normal projective connection. Moreover, they prove a general structure theorem on complex projective manifolds admitting a holomorphic normal…
We prove an equivalence of categories from formal complex structures with formal holomorphic maps to homotopy algebras over a simple operad with its associated homotopy morphisms. We extend this equivalence to complex manifolds. A complex…
Two Morrey-Sobolev inequalities (with support-bound and $L^1-$bound, respectively) are investigated on complete Riemannian manifolds with their sharp constants in $\mathbb R^n$. We prove the following results in both cases: $\bullet$ If…
In this paper, we study the prescribed $Q$-curvature problem on closed four-dimensional Riemannian manifolds when the total integral of the $Q$-curvature is a positive integer multiple of the one of the four-dimensional round sphere. This…
As a higher dimensional version of the theory of Morse functions, there have been various studies of smooth manifolds using generic smooth maps. As fundamental results, in these studies, they have found that inverse images of such maps…
In this paper, we investigate complete curvature-adapted submanifolds with maximal flat section and trivial normal holonomy group in symmetric spaces of compact type or non-compact type under certain condition, and derive the constancy of…
We introduce numerical algebraic geometry methods for computing lower bounds on the reach, local feature size, and the weak feature size of the real part of an equidimensional and smooth algebraic variety using the variety's defining…
We investigate {\bf explicit} universal estimate of finite Morse index solutions to polyharmonic equations. \,Differently to previous works \cite{BL2, DDF, fa, H1}, propose here a direct proof using a new interpolation inequality and a…
We study the higher (or sequential) topological complexity $\mathrm{TC}_s$ of manifolds with abelian fundamental group. We give sufficient conditions for $\mathrm{TC}_s$ to be non-maximal in both the orientable and non-orientable cases. In…
We exhibit some (compact and cusped) finite-volume hyperbolic four-manifolds M with perfect circle-valued Morse functions, that is circle-valued Morse functions $f\colon M \to S^1$ with only index 2 critical points. We construct in…
Closed (and simply-connected) manifolds whose dimensions are greater than 4 are classified via sophisticated algebraic and abstract theory such as surgery theory and homotopy theory. It is difficult to handle 3 or 4-dimensional closed…
Optimal weighted Sobolev-Lorentz embeddings with homogeneous weights in open convex cones are established, with the exact value of the optimal constant. These embeddings are non-compact, and this paper investigates the structure of their…
We show existence and uniqueness of solutions to the Monge-Ampere equation on compact almost complex manifolds with non-integrable almost complex structure.
We develop a new approach to $L^{\infty}$-a priori estimates for degenerate complex Monge-Amp\`ere equations on complex manifolds. It only relies on compactness and envelopes properties of quasi-plurisubharmonic functions. Our method allows…
We provide a new sufficient condition for strong invariance for differential inclusions, under very general conditions on the dynamics, in terms of a Hamiltonian inequality. In lieu of the usual Lipschitzness assumption on the…
We establish shape holomorphy results for general weakly- and hyper-singular boundary integral operators arising from second-order partial differential equations in unbounded two-dimensional domains with multiple finite-length open arcs.…
We study the compactness problem for moduli spaces of holomorphic supercurves which, being motivated by supergeometry, are perturbed such as to allow for transversality. We give an explicit construction of limiting objects for sequences of…
This paper studies first the differential inequalities that make it possible to build a global theory of pseudo-holomorphic functions in the case of one or several complex variables. In the case of one complex dimension, we prove that the…
We consider the Yamabe invariant of a compact orbifold with finitely many singular points. We prove a fundamental inequality for the estimate of the invariant from above, which also includes a criterion for the non-positivity of it.…
A Morse-Bott volume form on a manifold is a top-degree form which vanishes along a non-degenerate critical submanifold. We prove that two such forms are diffeomorphic (by a diffeomorphism fixed on the submanifold) provided that their…