What is he best known for?
The fields of study he is best known for:
- Mathematical analysis
- Geometry
- Pure mathematics
Mathematical analysis, Pure mathematics, Constant, Gravitational singularity and Scalar curvature are his primary areas of study.
When carried out as part of a general Mathematical analysis research project, his work on Conformal map is frequently linked to work in Analytical chemistry, therefore connecting diverse disciplines of study.
His work carried out in the field of Pure mathematics brings together such families of science as Carry, Metric and Singular solution.
Frank Pacard combines subjects such as Bounded function, Function, Gaussian curvature, Variable and Laplace operator with his study of Constant.
Specifically, his work in Scalar curvature is concerned with the study of Prescribed scalar curvature problem.
His biological study spans a wide range of topics, including Minimal surface and Delaunay triangulation.
His most cited work include:
- Construction of singular limits for a semilinear elliptic equation in dimension 2 (174 citations)
- Refined asymptotics for constant scalar curvature metrics with isolated singularities (162 citations)
- From Constant mean Curvature Hypersurfaces to the Gradient Theory of Phase Transitions (143 citations)
What are the main themes of his work throughout his whole career to date?
Frank Pacard mainly focuses on Mathematical analysis, Pure mathematics, Mean curvature, Constant and Scalar curvature.
His Mathematical analysis research integrates issues from Mean curvature flow, Nonlinear system and Moduli space.
His Pure mathematics study integrates concerns from other disciplines, such as Function and Yamabe problem.
His work deals with themes such as Hypersurface, Delaunay triangulation, Catenoid and Submanifold, which intersect with Mean curvature.
His study on Constant also encompasses disciplines like
- Carry most often made with reference to Blowing up,
- Geodesic most often made with reference to Riemannian manifold.
His studies deal with areas such as Manifold, Conformal map and Gravitational singularity as well as Scalar curvature.
He most often published in these fields:
- Mathematical analysis (57.89%)
- Pure mathematics (33.83%)
- Mean curvature (22.56%)
What were the highlights of his more recent work (between 2011-2017)?
- Mathematical analysis (57.89%)
- Allen–Cahn equation (11.28%)
- Mathematical physics (16.54%)
In recent papers he was focusing on the following fields of study:
Frank Pacard spends much of his time researching Mathematical analysis, Allen–Cahn equation, Mathematical physics, Pure mathematics and Mean curvature.
His work on Mathematical analysis is being expanded to include thematically relevant topics such as Invariant.
His work deals with themes such as Minimal surface, Moduli space, Function, Plane and Zero set, which intersect with Allen–Cahn equation.
His research in Mathematical physics intersects with topics in Symmetry, Nonlinear Schrödinger equation, Nonlinear system and Group.
The various areas that Frank Pacard examines in his Pure mathematics study include Geometry and Bounded function.
His Mean curvature research is multidisciplinary, incorporating elements of Critical point, Codimension, Curvature function and Isoperimetric inequality.
Between 2011 and 2017, his most popular works were:
- Torus action on S^n and sign changing solutions for conformally invariant equations (59 citations)
- Finite-energy sign-changing solutions with dihedral symmetry for the stationary nonlinear Schrödinger equation. (46 citations)
- Stable solutions of the Allen–Cahn equation in dimension 8 and minimal cones (38 citations)
In his most recent research, the most cited papers focused on:
- Mathematical analysis
- Geometry
- Algebra
Frank Pacard mostly deals with Pure mathematics, Zero set, Allen–Cahn equation, Mathematical analysis and Ball.
His Pure mathematics research incorporates elements of Geometry and Bounded function.
His Bounded function research includes themes of Overdetermined system, Surface, Constant, Mean curvature and Constant-mean-curvature surface.
His Zero set study also includes fields such as
- Affine transformation and related Space, Infinity, Structure and Manifold,
- Function which intersects with area such as Moduli space.
His work in the fields of Nonlinear Schrödinger equation overlaps with other areas such as Action.
His Ball research is multidisciplinary, incorporating perspectives in Minimal surface, Number theory, Combinatorics and Algebraic geometry.
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