Related papers: Quantitative unique continuation on conic manifold…

Using the Carleman linearization technique the continuous iteration of a mapping is studied. Based on the detailed analysis of the Carleman embedding matrix the precise mathematical meaning is given to such notion. The ordinary differential…

A Riemannian stochastic representation of model uncertainties in molecular dynamics is proposed. The approach relies on a reduced-order model, the projection basis of which is randomized on a subset of the Stiefel manifold characterized by…

In this note, we present new properties for a sequence arising in some refinements of Carleman's inequality. Our results extend some results of Yang [Approximations for constant e and their applications J. Math. Anal. Appl. 262 (2001)…

We prove index estimates for closed and free boundary CMC surfaces in certain $3$-dimensional submanifolds of some Euclidean space. When the mean curvature is large enough we are able to prove that the index of a CMC surface in an arbitrary…

In this paper, we prove the conic version of YTD conjecture on log Fano manifolds.

This paper explores recent progress related to constraint maps. Building on the exposition in [14], our goal is to provide a clear and accessible account of some of the more intricate arguments behind the main results in this work. Along…

In this note, we survey our recent work concerning cohomologies of harmonic bundles on quasi-compact Kaehler manifolds.

In this paper we extend a Calderon-Zygmund commutator-type estimate. This estimate enables us to prove an embedding result concerning weighted function spaces.

This paper investigates integer multiplication of continued fractions using geometric structures. In particular, this paper shows that integer multiplication of a continued fraction can be represented by replacing one triangulation of an…

Weighted quadratic estimates are proved for certain bisectorial firstorder differential operators with bounded measurable coefficients which are (not necessarily pointwise) accretive, on complete manifolds with positive injectivity radius.…

Some parts of stochastic analysis on curved spaces are revisted. A concise proof of the quasi-invariance of the Wiener measure on the path spaces over a Riemannian manifold is presented. The shifts are allowed to be in the Cameron-Martin…

We prove $L^p$ estimates for a continuous version of a dyadic quadrilinear form introduced by Kova\v{c} in [6]. This improves the range of exponents from the prequel [3] of the present paper.

In this paper, we introduce a new canonical connection on Riemannian manifold with a distribution. Moreover, as an application of the connection, we give a geometric proof of the Frobenius theorem.

In this article we collect results obtained by the authors jointly with other authors and we discuss old and new ideas. In particular we discuss singularities of the exponential map, completeness and homogeneity for Riemannian Hilbert…

This paper presents a new proof of the results regarding the continuity of weighted estimates with respect to the characteristic of the weight. Here we first prove the result in the dyadic case which is "easier" and then by the use of the…

This paper deals with the subject of infinitesimal variations of Euclidean submanifolds with arbitrary dimension and codimension. The main goal is to establish a Fundamental theorem for these geometric objects. Similar to the theory of…

We prove a new bound on the number of shared values of distinct meromorphic functions on a compact Riemann surface, explain a mistake in a previous paper on this topic, and give a survey of related questions.

We approximate smooth maps defined on non-compact totally real manifolds by holomorphic automorphisms of $\mathbb C^n$.

In this article we introduce an approach for studying the geodesic X-ray transform and related geometric inverse problems by using Carleman estimates. The main result states that on compact negatively curved manifolds (resp. nonpositively…

In this article, we prove a uniqueness result for a coefficient inverse problems regarding a wave, a heat or a Schr\"odinger equation set on a tree-shaped network, as well as the corresponding stability result of the inverse problem for the…