What is he best known for?
The fields of study he is best known for:
- Mathematical analysis
- Real number
- Geometry
Xavier Cabré mainly investigates Bounded function, Mathematical analysis, Pure mathematics, Weak solution and Laplace operator.
His Bounded function research incorporates elements of Discrete mathematics, Monotone polygon, Partial differential equation, Sobolev space and Domain.
He studies Mathematical analysis, focusing on Uniqueness in particular.
Many of his research projects under Pure mathematics are closely connected to Hamiltonian with Hamiltonian, tying the diverse disciplines of science together.
His Weak solution study combines topics in areas such as Mathematical physics, Pointwise, Unit sphere and Regular polygon.
His research in Laplace operator tackles topics such as Infinitesimal generator which are related to areas like Symmetry, Space, Combinatorics and Elliptic curve.
His most cited work include:
- Fully Nonlinear Elliptic Equations (1104 citations)
- Positive solutions of nonlinear problems involving the square root of the Laplacian (516 citations)
- Nonlinear equations for fractional Laplacians, I: Regularity, maximum principles, and Hamiltonian estimates (431 citations)
What are the main themes of his work throughout his whole career to date?
Xavier Cabré mostly deals with Mathematical analysis, Pure mathematics, Bounded function, Dimension and Domain.
His Mathematical analysis research integrates issues from Type and Constant.
He has researched Pure mathematics in several fields, including Mean curvature and Uniqueness.
His Bounded function study incorporates themes from Minimal surface, Regular polygon, Operator, Ball and Sobolev space.
He interconnects Class and Conjecture in the investigation of issues within Dimension.
His Domain research incorporates themes from Function and Open problem.
He most often published in these fields:
- Mathematical analysis (49.04%)
- Pure mathematics (45.19%)
- Bounded function (42.31%)
What were the highlights of his more recent work (between 2017-2021)?
- Pure mathematics (45.19%)
- Bounded function (42.31%)
- Mean curvature (19.23%)
In recent papers he was focusing on the following fields of study:
His primary scientific interests are in Pure mathematics, Bounded function, Mean curvature, Open problem and Domain.
The Pure mathematics study combines topics in areas such as Norm, Monotonic function and Uniqueness.
The various areas that Xavier Cabré examines in his Bounded function study include Minimal surface, Dimension and Conjecture.
The study incorporates disciplines such as Sobolev inequality, Mathematical analysis, Perimeter and Constant in addition to Mean curvature.
His work on Elliptic curve as part of general Mathematical analysis research is often related to Integer lattice, thus linking different fields of science.
His Open problem research is multidisciplinary, incorporating perspectives in Operator, Convex function and Laplace operator.
Between 2017 and 2021, his most popular works were:
- Curves and surfaces with constant nonlocal mean curvature: Meeting Alexandrov and Delaunay (54 citations)
- Stable solutions to semilinear elliptic equations are smooth up to dimension $9$ (26 citations)
- A gradient estimate for nonlocal minimal graphs (24 citations)
In his most recent research, the most cited papers focused on:
- Mathematical analysis
- Geometry
- Real number
His primary areas of study are Mean curvature, Bounded function, Constant, Mathematical analysis and Pure mathematics.
His Bounded function research includes elements of Sobolev inequality and Dimension.
His studies deal with areas such as Conjecture, Norm, Series, Domain and Corollary as well as Dimension.
He combines subjects such as Perimeter, Delaunay triangulation, Type and Elliptic curve with his study of Constant.
His research in Mathematical analysis is mostly concerned with Unit sphere.
His Harnack's inequality and Minimal surface study, which is part of a larger body of work in Pure mathematics, is frequently linked to Jacobi operator, bridging the gap between disciplines.
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