Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  present a numerical study for the first Dirichlet eigenvalue of certain classes of planar regions. Based on this,  propose new types of bounds and establish several conjectures regarding the dependence of this eigenvalue on the perimeter and the area.
['Pedro Antunes', 'Pedro Freitas']
I am writing a research paper on a idea New Bounds for the Principal Dirichlet Eigenvalue of Planar Regions
[{"from": "human", "value": "I am writing a research paper on a idea New Bounds for the Principal Dirichlet Eigenvalue of Planar Regions"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  present a numerical study for the first Dirichlet eigenvalue of certain classes of planar regions. Based on this,  propose new types of bounds and establish several conjectures regarding the dependence of this eigenvalue on the perimeter and the area."}]