相关论文: Local Uniqueness of the Circular Integral Invarian…

We prove an implicit function theorem for functions on infinite-dimensional Banach manifolds, invariant under the (local) action of a finite dimensional Lie group. Motivated by some geometric variational problems, we consider group actions…

We consider abstract inverse problems between infinite-dimensional Banach spaces. These inverse problems are typically nonlinear and ill-posed, making the inversion with limited and noisy measurements a delicate process. In this work, we…

In this paper we study an integral invariant which obstructs the existence on a compact complex manifold of a volume form with the determinant of its Ricci form proportional to itself, in particular obstructs the existence of a…

We present a formalisation of the existence and uniqueness theorems of integral curves of vector fields on Banach manifolds in the Lean theorem prover. First, we formalize properties of differential equations on Banach spaces (the…

We show how to compute the circular area invariant of planar curves, and the spherical volume invariant of surfaces, in terms of line and surface integrals, respectively. We use the Divergence Theorem to express the area and volume…

The famous Nash embedding theorem was aimed for in the hope that if Riemannian manifolds could be regarded as Riemannian submanifolds, this would then yield the opportunity to use extrinsic help. However, as late as 1985 (see \cite{G}) this…

We obtain a localized version of the configuration space integral for the Casson knot invariant, where the standard symmetric Gauss form is replaced with a locally supported form. An interesting technical difference between the arguments…

This study defines finite-type invariants for curves on surfaces and reveals the construction of these finite-type invariants for stable homeomorphism classes of curves on compact oriented surfaces without boundaries. These invariants are a…

This is the fourth in a series of papers where we prove a conjecture of Deser and Schwimmer regarding the algebraic structure of ``global conformal invariants''; these are defined to be conformally invariant integrals of geometric scalars.…

We derive some integral inequalities for holomorphic maps between complex manifolds. As applications, some rigidity and degeneracy theorems for holomorphic maps without assuming any pointwise curvature signs for both the domain and target…

First introduced to describe surfaces embedded in $\mathbb{R}^3$, the Willmore invariant is a conformally-invariant extrinsic scalar curvature of a surface that vanishes when the surface minimizes bending and stretching. Both this invariant…

A regularization procedure developed in [1] for the integral curvature invariants on manifolds with conical singularities is generalized to the case of squashed cones. In general, the squashed conical singularities do not have rotational…

In this paper we define the notion of slow divergence integral along sliding segments in regularized planar piecewise smooth systems. The boundary of such segments may contain diverse tangency points. We show that the slow divergence…

This paper provides a self-contained exposition of coorbit spaces associated to integrable group representations and quasi-Banach function spaces, and at the same time extends and simplifies previous work. The main results provide an…

We show an analogue of the Klain-Schneider theorem for valuations that are invariant under rotations around a fixed axis, called zonal. Using this, we establish a new integral representation of zonal valuations involving mixed area measures…

We provide sharp lower bounds for the multiplicity of a local holomorphic foliation defined in a complex surface in terms of data associated to a germ of invariant curve. Then we apply our methods to invariant curves whose branches are…

Consider a smooth projective curve and a given embedding into projective space via a sufficiently positive line bundle. We can form the secant variety of $k$-planes through the curve. These are singular varieties, with each secant variety…

This is the last in a series of papers where we prove a conjecture of Deser and Schwimmer regarding the algebraic structure of ``global conformal invariants''; these are defined to be conformally invariant integrals of geometric scalars.…

The structure of subspaces of a Hilbert space that are invariant under unitary representations of a discrete group is related to a notion of Hilbert modules endowed with inner products taking values in spaces of unbounded operators. A…

An integral invariant model derived from the coupling of the transport equation and its adjoint equation is investigated.Despite extensive research on the numerical implementation of this model,no studies have yet explored the…