13 citations · 32 across the 22 of their papers we have counts for
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Beyond Harnack Amoeba Boundaries
Mounir Nisse
We construct smooth irreducible plane curves whose complete amoeba contour is a smooth embedded curve equal to the amoeba boundary, although the curves are not torically equivalent…
The CR Nirenberg Problem, Part II: Existence and Topological Degree
Jiechen Qiang, Zhongwei Tang, Heming Wang
This paper is a continuation of Part~I \cite{QTWPartI}, where blow-up analysis and compactness results for the CR Nirenberg problem were established. We prove some existence and de…
Beyond Harnack Rigidity
Mounir Nisse
The boundary of a plane amoeba is always contained in its contour, and equality is a characteristic feature of simple Harnack curves. We show that the converse fails, even under st…
On the Analyticity of Amoeba Contours
Mounir Nisse
The contour of an amoeba records the critical values of the logarithmic map and forms a fundamental interface between complex algebraic geometry and real-analytic geometry. Buildin…
Cusps and nodes of Amoeba Contours
Mounir Nisse
We establish new Newton-polygon bounds for the singularities of amoeba contours of smooth plane curves. Our cusp estimate refines the degree-four bound of Lang--Shapiro--Shustin, r…
Singularities of Amoeba Contours
Mounir Nisse
We give explicit real-algebraic equations for computing the singularities of amoeba contours, separating degeneracies of the logarithmic critical locus from coincidences of distinc…
Sparse Bounds for Amoeba Contours
Mounir Nisse
We derive new upper bounds for the real degree of the contour of the amoeba of algebraic curves and hypersurfaces. Our approach refines the Pfaffian method of Lang--Shapiro--Shusti…
Contour Degree of Amoebas of Complete Intersections
Mounir Nisse
We establish the first universal upper bounds for the real degree of the contour of the amoeba of a smooth complete intersection in the algebraic torus. Our approach extends the Pf…